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Ryan
Ryan, Engineer
Category: Calculus and Above
Satisfied Customers: 7584
Experience:  B.S. in Civil Engineering
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3. You are given the sample mean and the sample standard deviation.

Customer Question

3. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If the convenient, use technology to construct the confidence intervals.

A random sample of 38 eight-ounce servings of different juice drinks has a mean of 86.4 calories and a standard deviation of 46.9 calories.

The 90% confidence interval is ( _____,_____). (Round to one decimal places as needed.)
The 95% confidence interval is ( _____,_____). (Round to two decimal places as needed.)





4. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals or the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.

A random sample of 45 home theater systems has a mean price of $129.00 and a standard deviation of $18.20

Construct a 90% confidence interval for the population mean.

The 90% confidence interval is (____,____).
(Round to two decimal places as needed.)

Construct a 95% confidence interval for the population mean.

The 95% confidence interval is (____,____).
(Round to two decimal places as needed.)



5. Construct the confidence interval for the population mean µ.
C= 0.95, x=16.7, s=5.0, and n=35

A 95% confidence interval for µ is _____, ______ (Round to two decimal places as needed.)


6. Construct the indicated confidence interval for the population mean µ using (a) a t-distribution. (b) If you had incorrectly used a normal distribution, which interval would be wider?
C= 0.99, x=14.8, s=2.0, n=9

(a) The 99% confidence interval using a t-distribution is (____,_____).
(Round to one decimal place as needed.)



7. In the following situation, assume the random variable is normally distributed and use a normal distribution or a t-distribution to construct a 90% confidence interval for the population mean. If convenient, use technology to construct the confidence interval.

(A) In a random sample of 10 adults from a nearby county, the mean waste generated
Per person per day was 3.77 pounds and the standard deviation was 1.16 pounds.
(B) Repeat part (a), assuming the same statistics came from a sample size of 600. Compare the results.

(a) For the sample of 10 adults, the 90% confidence intervals is (____,____).
(Round to two decimal places as needed.)

(b) For the sample of 600 adults, the 90% confidence intervals is (____,____).
(Round to two decimal places as needed.)


15. Use the given confidence interval to find the margin of error and the sample proportion. (0.728,0.754)

E=_____ (Type an integer or a decimal)
P=_____(Type an integer or a decimal)









16. In a survey of 639 males ages 18-64, 394 say they have gone to the dentist in the past year.

Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals.

The 90% confidence interval for the population proportion p is _____ , _____.
(Round the final answers to the nearest thousandth as needed. Round all intermediate values to the nearest thousandth as needed.)

The 95% confidence interval for the population proportion p is _____ , _____.
(Round the final answers to the nearest thousandth as needed. Round all intermediate values to the nearest thousandth as needed.)


20. The table shows the results of a survey in which separate samples of 400 adults each from the East, South, Midwest, and West were asked if traffic congestion is a serious problem in their community. Complete parts (a) and (b)

(a)Construct a 95% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem.
The 95% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem is (___,___) (Round to three decimal places as needed.)


(b) Construct a 95% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem.
The 95% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem is (___,___) (Round to three decimal places as needed.)

East: 35%
South:32%
Midwest:27%
West:54%
Submitted: 2 years ago.
Category: Calculus and Above
Expert:  Ryan replied 2 years ago.
Hi,

Thank you for using JustAnswer.

I'll be happy to help you with these problems. Do you need the calculations, or just the final answers?

Thanks,

Ryan
Customer: replied 2 years ago.
Just The final answers

Thank You
Expert:  Ryan replied 2 years ago.
Hi,

Ok. I'll post them as soon as I can. Should only take 10-15 minutes.

Thanks,

Ryan
Expert:  Ryan replied 2 years ago.
Hi,

Here are the solutions:

ConfidenceIntervals

Please feel free to ask if you have questions about any of these solutions.

Thanks,

Ryan
Customer: replied 2 years ago.
I made a mistake on these 2 right here .....




5.Construct the confidence interval for the population mean µ.
C= 0.95, x=15.8, s=6.0, and n=85

A 95% confidence interval for µ is _____, ______ (Round to one decimal places as needed.)



20. The table shows the results of a survey in which separate samples of 400 adults each from the East, South, Midwest, and West were asked if traffic congestion is a serious problem in their community. Complete parts (a) and (b)

(a)Construct a 95% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem.
The 95% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem is (___,___) (Round to three decimal places as needed.)


(b) Construct a 95% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem.
The 95% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem is (___,___) (Round to three decimal places as needed.)

East: 36%
South:33%
Midwest:28%
West:53%



Expert:  Ryan replied 2 years ago.
Hi,

For #5: 14.5, 17.1

For #20:

a) 0.481, 0.579

b) 0.284, 0.376


Thanks,

Ryan
Ryan, Engineer
Satisfied Customers: 7584
Experience: B.S. in Civil Engineering
Ryan and other Calculus and Above Specialists are ready to help you
Customer: replied 2 years ago.
Hi Ryan

There is a little quiz that i have to do now i think it is only 12 multiple choice and 3 short answer. can u help me with that?
Expert:  Ryan replied 2 years ago.
Hi,

I'll certainly try. It's hard to say without knowing anything about the type of questions that might be asked.

Ryan
Customer: replied 2 years ago.
okay ryan

do u want me to go ahead and post them?

my timing on the quiz is 2hrs
Expert:  Ryan replied 2 years ago.
Hi,

Sure thing. I'm ready when you are.

Ryan
Customer: replied 2 years ago.
1. (TCO 6) In the standard normal distribution the means is always (Points : 3)
0
1
2
none of these

2. (TCO 6) The area under the standard normal curve is (Points : 3)
0
1
2
none of these

3. (TCO 6) If John gets an 80 on a physics test where the mean is 85 and the standard deviation is 3, where does he stand in relation to his classmates? (Points : 3)
He is in the top 5%.
He is in the top 10%.
He is in the bottom 5%.
He is the bottom 1%.

4. (TCO 6) In a normal distribution with mu = 25 and sigma = 6, what number corresponds to z = 3? (Points : 3)
40
43
46
none of these

5. (TCO 6) Let’s assume you have taken 100 samples of size 49 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 16. (Points : 3)
0.571
0.429
0.327
0.107

6. (TCO 6) The area to the left of ‘z’ is 0.0681. What z-score corresponds to this area? (Points : 3)
-1.40
1.49
-1.49
none of these

7. (TCO 6) Find P(9 < x < 22) when mu = 20 and sigma = 5. (Points : 3)
0.6554
0.6415
0.0139
0.3585

8. (TCO 7) What is the critical z-value that corresponds to a confidence level of 86%? (Points : 3)
approximately 1.48
approximately 1.55
approximately 1.75
none of these

9. (TCO 7) Compute the population mean margin of error for a 90% confidence interval when sigma is 4 and the sample size is 36. (Points : 3)
+/- 1.3066…
+/- 1.0966...
+/- 1.7166...
none of these

10. (TCO 7) A standard IQ test has a mean of 98 and a standard deviation of 16. We want to be 99% certain that we are within 8 IQ points of the true mean. Determine the sample size. (Points : 3)
16
27
26
none of these

11. (TCO 7) A private medical clinic wants to estimate the true mean annual income of its patients. The clinic needs to be within $500 of the true mean. The clinic estimates that the true population standard deviation is around $2,300. If the confidence level is 95%, find the required sample size in order to meet the desired accuracy. (Points : 6)
195
80
82
101

12. (TCO 7) An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor wants to be within 10% of the true proportion when using a 95% confidence level. How many files must the auditor sample? No estimate of the proportion is available, so use 0.5 for the population proportion. (Points : 6)
90
97
105
180




13. (TCO 7) Interpret a 90% confidence interval of (4.355, 4.445) for a population mean. (Points : 6)


14. (TCO 7) A nursing school wants to estimate the true mean annual income of its alumni. It randomly samples 200 of its alumni. The mean annual income was $52,500 with a standard deviation of $1,800. Find a 95% confidence interval for the true mean annual income of the nursing school alumni. Write a statement about the confidence level and the interval you find. (Points : 6)


(TCO 7) An auditor wants to estimate what proportion of a bank’s commercial loan files are incomplete. The auditor randomly samples 80 files and finds 12 are incomplete. Using a 95% confidence interval, estimate the true proportion of incomplete files for ALL the bank’s commercial loans. Write a statement about the confidence level and the interval you find. (Points : 6)
Expert:  Ryan replied 2 years ago.
Hi,

Ok, got 'em. I'll post the solutions as soon as I can work through the problems.

Thanks,

Ryan
Customer: replied 2 years ago.
Thank you Ryan
Expert:  Ryan replied 2 years ago.
Hi again,

Here are the solutions:

Stats


Thanks,

Ryan
Customer: replied 2 years ago.
Hi Ryan

There are some multiple choice questions that i have to do for a test and i was wonder if u can help me?


Expert:  Ryan replied 2 years ago.
Hi,

I'll be happy to take a look at them. Please post them at your convenience.

Thanks,

Ryan
Customer: replied 2 years ago.
Thank You Ryan




Page 1



1. (TCO 9) The hours of study and the final exam grades have this type of relationship:
ŷ = 6.75(hours) + 37.45. Based on this linear regression equation, estimate the expected grade for a student spending 8 hours studying. Round your answer to two decimal places. (Points : 6)
91.45
54
93.42
89.45

2. (TCO 5) A company produces electronic equipments claims that 98% of their products never need any kind of maintenance. We selected 10 of their products and we wanted to know the probability that 8 of them never need maintenance. Choose the best answer of the following: (Points : 6)
This is an example of a Poisson probability experiment
This is an example of a Binomial probability experiment
This is neither a Poisson nor a Binomial probability experiment
Not enough information to determine the type of experiment

3. (TCO 5) Microfracture knee surgery has a 75% chance of success on patients with degenerative knees. The surgery is performed on 5 patients. Find the probability of the surgery being successful on more than 3 patients? (Points : 6)
0.487304
0.367188
0.632813
0.762695

4. (TCO 5) It has been recorded that 10 people get killed by shark attack every year. What is the probability of having 7 or 8 people get killed by shark attack this year? (Points : 6)
0.130141
0.202678
0.220221
0.797321





5. (TCO 2) The mode teaching hours for a full time faculty at a state university is eight hours per week. What does this tell you about the typical teaching hours for full time faculty at that university? (Points : 6)
Half the full time faculties teach less than eight hours per week while half teaches more than eight hours per week.
The average teaching hours for full time faculty is eight hours per week.
More full time faculty teaches eight hours per week than any other number of teaching hours.
The number of teaching hours for full time faculty in not very consistent because eight is such a low number.

6. (TCO 6) Assuming that the data are normally distributed with a mean of 45 and a standard deviation of 3.25, what is the z-score for a value of 40? (Points : 6)
1.54
2.38
-1.36
-1.54

7. (TCO 8) The mean hours of Internet usage by adults in the US in claimed to be less than 25 hours per week. A hypothesis test is performed at a level of significance of 0.05 with a P-value of 0.11. Choose the best interpretation of the hypothesis test. (Points : 6)
Reject the null hypothesis; there is enough evidence to reject the claim that the mean of hours Internet usage by adults in the US is 25 hours.
Reject the null hypothesis; there is enough evidence to support the claim that the mean hours Internet usage by adults in the US is 25 hours per week.
Fail to reject the null hypothesis; there is not enough evidence to reject the claim that the mean hours of Internet usage by adults in the US is 25 hours per week.
Fail to reject the null hypothesis; there is not enough evidence to support the claim that the mean hours of Internet usage by adults in the US is 25 hours per week.





8. (TCO 8) A result of an entry level exam reveals that 22% of students fail that exam.
In a hypothesis test conducted at a level of significance of 2%, a P-value of 0.045 was obtained. Choose the best interpretation of the hypothesis test. (Points : 6)
Fail to reject the null hypothesis; there is not enough evidence to reject the claim that 22% of students fail the entry level exam.
Fail to reject the null hypothesis; there is not enough evidence to support the claim that 22% of students fail the entry level exam.
Reject the null hypothesis; there is enough evidence to reject the claim that 22% of students fail the entry level exam.
Reject the null hypothesis; there is enough evidence to support the claim that 22% of students fail the entry level exam.

9. (TCO 2) You want to buy light bulbs and you want to choose between two vendors. Vendor A’s light bulbs have a mean life time of 800 hours and a standard deviation of 175 hours. Vendor B’s light bulbs also have a mean life time of 800 hours, but a standard deviation of 225 hours. You want light bulbs that have more life time consistency, which vendor will you purchase from? (Points : 6)
Vendor A because you will be more likely get light bulbs with the same life time
Vendor B because you will be more likely get light bulbs with the same life time
Either one because both produce light bulbs with the same mean life time.
Neither one because a mean height of 800 inches is too short for a light bulb.

10. (TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 45% red, 35% blue, 15% yellow, and 5% green. If you are to select one ball at random. Find the expected value of your winning amount if the payments are set to be $5, $15, $25, $60 for red, blue, yellow and green ball respectively.


Winning amount
5
15
25
60
Probability
45%
35%
15%
5%
(Points : 6)
The expected winning amount is $28.50
The expected winning amount is $14.25
The expected winning amount is $25.50
The expected winning amount is $11.25

11. (TCO 3) The grades of 22 students are listed below. Use the stem & leaf to determine the shape of the distribution. Choose the best answer.
4 | 7 5
5 | 1 7 5
6 | 5 6 7 8 9
7 | 1 6 7 8 8 9
8 | 2 4 7 6
9 | 4 7

(Points : 6)
The data is symmetric
The data is skewed to the right
The data is skewed to the left
The data is bimodal

12. (TCO 1) A researcher is interested in studying people’s mean age in a certain region. If the population standard deviation is known to be 8 years and 1.5 year of error margin is allowed, find the minimum simple size the researcher needs to use, knowing that he is going to conduct his study using 95% confidence level. (Points : 6)
Sample Size = 77
Sample Size = 25
Sample Size = 210
Sample Size = 110

13. (TCO 6) Horse race time is found to be normally distributed with a mean value of 18 minutes and a standard deviation of 4 minutes. Horses whose race time is in the top 6% will not be eligible to participate in a second round. What is the lowers race time that makes a horse losses his eligibility to participate in a second round? (Points : 6)
26.6
11.8
24.2
20.3

14. (TCO 5) A class containing 15 students 5 of them are females. In how many ways can we select a group of 4 male students? (Points : 6)
260
120
5040
210

15. (TCO 6) Research shows that the life time of Everlast automobile tires is normally distributed with a mean value of 60,000 miles and a standard deviation of 5,000 miles. What is the probability of having a tire that lasts more than 67,000 miles? (Points : 6)
0.9192
0.0808
1.40
0.0793

16. (TCO 10) A research shows that employee salaries at company XYX, in thousands of dollars, are given by the equation y-hat= 48.5 + 2.2 a + 1.5 b where ‘a’ is the years of experience, and ‘b’ is the education level in years. In thousands of dollars, predict the salary for an employee with 7 years experience and 12 years education level. (Points : 6)
52.2
81.9
67.5
63.9

17. (TCO 9) For the graph below, choose the statement that best describes the relationship between the variables.


(Points : 6)
As hours of absences increases, grades decreases.
As hours of absences decreases, grades increases.
As hours of absences increases, grades increases.
There is no relationship between hours of absences and grades.
Expert:  Ryan replied 2 years ago.
Hi,

Thanks. I'll post the solutions as soon as I work through these.

Ryan
Customer: replied 2 years ago.
Okay thank you ryan, i am on a timing of 2hrs
Expert:  Ryan replied 2 years ago.
Hi,

Ok, that shouldn't be a problem.

Ryan
Expert:  Ryan replied 2 years ago.
Hi again,

Are there just these 17 questions? I noticed the "Page 1" line near the top, which implies that there might be a "Page 2"...

I just want to make sure that you post didn't get cut off for exceeding the maximum character length.

Thanks,

Ryan
Customer: replied 2 years ago.
Hi Ryan

17 is all the questions
Expert:  Ryan replied 2 years ago.
Hi,

Ok, thanks.

I just noticed that problem #17 refers to a graph. I can't answer the question without the graph. Can you post a screenshot of the graph?

I have the rest of them done.

Thanks,

Ryan
Customer: replied 2 years ago.
I will do number 17 on my own , i really don't know how to screenshot on this mac laptop lol

Thank you
Expert:  Ryan replied 2 years ago.
Hi,

Ok, here are the first 16:

Stats

FYI, to take a screenshot on a Mac, hold down the command and shift keys, and press the number 3. You will hear a camera click sound (unless the volume is muted). An image of the screen will be saved to the desktop. It will be named "Screenshot" with the date and time added to it.

If you want to be more selective, press 4 instead of 3. A set of cross-hairs will be shown. You can then click and drag to select a rectangle that includes just the part of the screen that you want to capture.

It's quite easy. I use it every day.

If you want to try it and post the graph for the last problem, go right ahead. I'll be happy to answer that one.

Thanks,

Ryan
Ryan, Engineer
Satisfied Customers: 7584
Experience: B.S. in Civil Engineering
Ryan and other Calculus and Above Specialists are ready to help you
Customer: replied 2 years ago.
Hi Ryan i got it screenshot but how do i get it here now?
Expert:  Ryan replied 2 years ago.
Hi,

You can upload it to a free file-sharing site like mediafire.com or sendspace.com. Once you have it uploaded, you can copy the sharing link and then paste it into a reply here. (It sounds harder than it it. Once you've done it a few times, it only takes a minute.)

Ryan
Customer: replied 2 years ago.
Hi Ryan

I think i got it download:

http://www.mediafire.com/?dnpgczmcxoz97a5
Expert:  Ryan replied 2 years ago.
Hi,

Yes, that worked. Smile

The answer for #17 is:

A. As the hours of absences increases, grades decreases.


Thanks,

Ryan
Ryan, Engineer
Satisfied Customers: 7584
Experience: B.S. in Civil Engineering
Ryan and other Calculus and Above Specialists are ready to help you
Customer: replied 2 years ago.
Thank you so much ryan for helping me out and thank you for showing me something new on my laptop i really appreciate it.
Expert:  Ryan replied 2 years ago.
Hi,

You're quite welcome. I'm very glad that I could help.

Thanks,

Ryan
Customer: replied 2 years ago.
Hello Ryan it's me again,


I was wondering if you can help me with 7 math problems today
Expert:  Ryan replied 2 years ago.
Hi,

I'll be happy to take a look at them.

Ryan
Customer: replied 2 years ago.
Hi Ryan my timing is 2hrs and 30mins



1. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.
Company X claims that the average salary for an entry level employee is $35,000 (Points : 8)



2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 20 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 21.25 minutes and the standard deviation was found to be 4.3 minutes. Is there evidence to reject the manager’s claim at alpha =.01? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)



3. (TCO 5) A researcher found that 85% of customers who make purchase at a department store are pleased with the store customer service. We asked 20 customers whether or not they are please with the store customer service.


(a) Is this a binomial experiment? Explain how you know.
(b) Use the correct formula to find the probability that, out of 20 customers, exactly 12 of them are pleased with the store customer service. Show your calculations or explain how you found the probability. (Points : 20)



4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20.
(a) Find the probability of having a utility bill between 135 and 170.
(b) Find the probability of having a utility bill less than $135.
(c) Find the probability of having a utility bill more than $180. (Points : 20)



5. (TCO 8) A Mall manager claims that in average every customer spends $37 per a single visit to the mall. To test this claim, you took a sample of 64 customers and found the sample mean to be $34 and the sample standard deviation to be $5. At alpha = 0.05, test the Mall’s manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)



6. (TCO 7) A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 60 businesses, he found the mean number of transaction per month to be 38 and the standard deviation to be 8.5 transactions.
(a) Find a 95% confidence interval for the mean number of business transactions per month. Show your calculations and/or explain the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it. (Points : 20)



7. (TCO 7) A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 600 products, he found 45 defective products.


(a) Find a 99% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it. (Points : 20)



8. (TCO 2) The ages of 10 students are listed in years:{ 17,20,18,24,21,26,29,18,22,28}


(a) Find the mean, median, mode, sample variance, and range.
(b) Do you think that this sample might have come from a normal population? Why or why not? (Points : 20)


Expert:  Ryan replied 2 years ago.
Hi,

Do you need to show work for these?

Ryan
Customer: replied 2 years ago.
yes
Expert:  Ryan replied 2 years ago.
Hi,

Yeah, I figured that out once I started reading through them.

No problem. I'm working on them now.

Thanks,

Ryan
Customer: replied 2 years ago.
ok thank you ryan
Expert:  Ryan replied 2 years ago.
Hi,

Just to update you, I have two left to complete.

Ryan
Customer: replied 2 years ago.
cool
Expert:  Ryan replied 2 years ago.
Hi,

Here are the solutions:

Stats

Thanks,

Ryan
Customer: replied 2 years ago.
Hi Ryan

can you post the answers here because word is not letting me copy them. and i only have 19 more mins
Expert:  Ryan replied 2 years ago.
Hi,

I'll try, but I don't know if it will all fit in one answer. If it doesn't, then I'll post it in parts.

Ryan
Customer: replied 2 years ago.
okay
Expert:  Ryan replied 2 years ago.
Hi,

The equations that were written using Equation Editor aren't going to copy. I'll have to edit the file to post it here. I'll do it as quick as I can.

Ryan
Customer: replied 2 years ago.
okay thank you
Expert:  Ryan replied 2 years ago.
Hi,

Here's what I have (sorry, it's not going to be very pretty):

Thanks,

Ryan

1. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.
Company X claims that the average salary for an entry level employee is $35,000 (Points : 8)



H0: µ = 35,000 (Claim)

Ha: µ ≠ 35,000


2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 20 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 21.25 minutes and the standard deviation was found to be 4.3 minutes. Is there evidence to reject the manager's claim at alpha =.01? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)



Hypotheses:



H0: µ ≤ 20 (Claim)

Ha: µ > 20



Critical value:



For a right-sided, one-tailed test at a = 0.01, the critical value is z = 2.326



Test value:



z = (21.25 - 20) / (43 / √49) = 2.0349





Decision:



Since the test value is less than the critical value, do not reject the null

hypothesis.



Summary:



There is not sufficient evidence to reject the manager's claim.






3. (TCO 5) A researcher found that 85% of customers who make purchase at a department store are pleased with the store customer service. We asked 20 customers whether or not they are please with the store customer service.


(a) Is this a binomial experiment? Explain how you know.



Yes, because it meets the requirements of a binomial experiment:



1) There are only two outcomes for each trial ("pleased" or "not pleased").



2) There are a fixed number of trials (20 customers).



3) The probability of success is constant for each trial (0.85).



4) The trials are independent (we are assuming that one customer is

independent of another, and that one customer's answer is not influenced

by another customer's response.)




(b) Use the correct formula to find the probability that, out of 20 customers, exactly 12 of them are pleased with the store customer service. Show your calculations or explain how you found the probability. (Points : 20)

P(12,20) = [20! /[(20 - 10)!(12!)]](0.85)^12(1 - 0.85)^8 = 0.0046





4. (TCO 6) The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20.
(a) Find the probability of having a utility bill between 135 and 170.



z1 = (135 - 150)/20 = -0.75



z2 = (170 - 150)/20 = 1.00



P(135 < x < 170) = P(-0.75 < z < 1.00) = P(z < 1.00) - P(z < -0.75)



= 0.8413 - 0.2266



= 0.6147





(b) Find the probability of having a utility bill less than $135.



z = (135 - 150) / 20 = -0.75



P(x < 135) = P(z < -0.75) = 0.2266





(c) Find the probability of having a utility bill more than $180. (Points : 20)

z = (180 - 150) / 20 = 1.50



P(x > 180) = P(z > 1.50) = 0.0668










5. (TCO 8) A Mall manager claims that in average every customer spends $37 per a single visit to the mall. To test this claim, you took a sample of 64 customers and found the sample mean to be $34 and the sample standard deviation to be $5. At alpha = 0.05, test the Mall's manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

Hypotheses:



H0: µ = 37 (Claim)



Ha: µ ≠ 37



Critical value:



For a two-tailed test at a = 0.05, the critical value is zcrit = ±1.96



Test value:



z(test) = (34 - 37) / (5 / √64) = -4.80





Decision:



Since the test value is less than the negative critical value, reject the

null hypothesis.



Summary:



There is sufficient evidence at the 0.05 level of significance to reject

the manager's claim.






6. (TCO 7) A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 60 businesses, he found the mean number of transaction per month to be 38 and the standard deviation to be 8.5 transactions.


(a) Find a 95% confidence interval for the mean number of business transactions per month. Show your calculations and/or explain the process used to obtain the interval.



The confidence interval is calculated from the formula:



(x-bar) - z(alpha/2) * (s/√n) < µ < (x-bar) + z(alpha/2) * (s/√n)



where x-bar is the sample mean, s is the sample standard deviation, n is the sample size, and z(alpha/2) is the critical value for a two-tailed test at level of significance alpha.



For a 95% confidence interval, alpha = 0.05, and the critical value is 1.96.



The confidence interval is then:



38 - (1.96)(8.5/√60) < µ < 38 + (1.96)(8.5/√60)



38 - 2.1508 < µ < 38 + 2.1508



35.8492 < µ < 40.1508



The 95% confidence interval is (35.85, 40.15).


(b) Interpret this confidence interval and write a sentence that explains it. (Points : 20)



The interpretation of the confidence interval is that if repeated samples are drawn from this population, the sample mean would be within the limits of the

confidence interval for approximately 95% of the samples.

This is somewhat analogous to saying that we can be 95% certain that the true mean value of the population is between 35.85 and 40.15.







7. (TCO 7) A company's CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 600 products, he found 45 defective products.


(a) Find a 99% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.



p-hat = 45/600 = 0.075



The confidence interval is calculated from:



p-hat - z(alpha/2)√[p-hat(1-p-hat) / n] < p < p-hat + z(alpha/2)√[p-hat(1-p-hat) / n]



For a 99% confidence interval, z(alpha/2) = 2.576



The confidence interval is then:



0.075 - (2.576)√(0.075(1 - 0.075)/600) < p < 0.075 + (2.576)√(0.075(1 - 0.075)/600)



0.0473 < p < 0.1027





The 99% confidence interval is (0.05, 0.10).



(b) Interpret this confidence interval and write a sentence that explains it. (Points : 20)

The interpretation of this confidence interval is that if repeated samples were

drawn from this population, the proportion of defects found would be within

the limits of the confidence interval approximately 99% of the time.



As stated in the previous problem, this is somewhat analogous to saying that the

we can be 99% certain that the true proportion of defects in this population is

between 0.05 and 0.10.







8. (TCO 2) The ages of 10 students are listed in years:{ 17,20,18,24,21,26,29,18,22,28}


(a) Find the mean, median, mode, sample variance, and range.



Mean =(17 + 20 + 18 + 24 + 21 + 26 + 29 + 18 + 22 + 28) / 10 = 22.3



Median:



The ordered data is {17, 18, 18, 20, 21, 22, 24, 26, 28, 29}



The middle values are 21 and 22. The median is the average of these two

values:



Median = (21 + 22) / 2 = 21.50





Mode = 18



Sample variance = √166.10/9 = 4.2960







Range = Highest value - lowest value = 29 - 17 = 12





(b) Do you think that this sample might have come from a normal population? Why or why not? (Points : 20)



For this sample, mode < median < mean, which fits the pattern of a positively

skewed distribution. A normal population should have a symmetric distribution,

so it is possible that this sample is not drawn from a normal population.

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