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. (TCO 8) For the...

. (TCO 8) For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim.

A car manufacturer claims that their cars makes at least 35 miles per gallon of fuel. (Points : 8)

2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 18 minutes. A random sample of 36 home delivery pizzas was collected. The sample mean was found to be 19.25 minutes and the standard deviation was found to be 3.3 minutes. Is there evidence to reject the manager’s claim at alpha =.02? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

3. (TCO 5) At a jewelry store, the probability for a customer to make a purchase when entering the store is 35%. We asked 25 customers enter the store whether they made a purchase or not.

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

(b) Use the correct formula to find the probability that, out of 25 customers, exactly 10 of them make a purchase. 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 $130 and a standard deviation of $15.

(a) Find the probability of having a utility bill between 100 and 150.

(b) Find the probability of having a utility bill less than $90.

(c) Find the probability of having a utility bill more than $160. (Points : 20)

5. (TCO 8) A Mall manager claims that in average every customer spends $42 per a single visit to the mall. To test this claim, you took a sample of 49 customers and found the sample mean to be $39 and the sample standard deviation to be $9. 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:{ 18,20,27,24,29,21,28,19,22,28}

(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)

9. (TCO 2) A bank is going to choose between two systems A and B which helps in measuring customers waiting time. During the trial period, both systems showed an average waiting time of 10 minutes. Type A showed a standard deviation of 2 minutes while type B showed a standard deviation of 4 minutes. Which of the two systems the bank should choose? (Points : 6)

System A because in shows more consistency in measuring the average waiting time.

System B because in shows more consistency in measuring the average waiting time.

Either because their mean waiting time is the same in both systems.

Neither because the given information is not enough to make a decision

10. (TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 40% red, 35% blue, 20% 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 $0, $5, $25, $70 for red, blue, yellow and green ball respectively.

Winning amount 0 5 25 70

Probability 40% 35% 20% 5%

(Points : 6)

The expected winning amount is $25.50

The expected winning amount is $14.50

The expected winning amount is $12.25

The expected winning amount is $10.25

11. (TCO 3) The grades of 20 students are listed below. Use the stem & leaf to determine the shape of the distribution. Choose the best answer.

4 | 4

5 | 6 8

6 | 5 7 9

7 | 1 5 7 8 8 9

8 | 3 4 5 7 8 8 9

9 | 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

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 20 students 8 of them are females. In how many ways can we select a group of 5 male students? (Points : 6)

56

792

6720

95040

15. (TCO 6) Research shows that the life time of Everlast automobile tires is normally distributed with a mean value of 70,000 miles and a standard deviation of 7,000 miles. What is the probability of having a tire that lasts more than 80,000 miles? (Points : 6)

0.9236

0.0778

0.0764

1.43

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 10 years experience and 14 years education level. (Points : 6)

52.2

72.5

70.5

91.5

17. (TCO 9) The estimated value for the correlation coefficient for this graph might be

(Points : 6)

-0.91

0.50

0.91

-0.50

A car manufacturer claims that their cars makes at least 35 miles per gallon of fuel. (Points : 8)

2. (TCO 11) A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 18 minutes. A random sample of 36 home delivery pizzas was collected. The sample mean was found to be 19.25 minutes and the standard deviation was found to be 3.3 minutes. Is there evidence to reject the manager’s claim at alpha =.02? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. (Points : 20)

3. (TCO 5) At a jewelry store, the probability for a customer to make a purchase when entering the store is 35%. We asked 25 customers enter the store whether they made a purchase or not.

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

(b) Use the correct formula to find the probability that, out of 25 customers, exactly 10 of them make a purchase. 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 $130 and a standard deviation of $15.

(a) Find the probability of having a utility bill between 100 and 150.

(b) Find the probability of having a utility bill less than $90.

(c) Find the probability of having a utility bill more than $160. (Points : 20)

5. (TCO 8) A Mall manager claims that in average every customer spends $42 per a single visit to the mall. To test this claim, you took a sample of 49 customers and found the sample mean to be $39 and the sample standard deviation to be $9. 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:{ 18,20,27,24,29,21,28,19,22,28}

(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)

9. (TCO 2) A bank is going to choose between two systems A and B which helps in measuring customers waiting time. During the trial period, both systems showed an average waiting time of 10 minutes. Type A showed a standard deviation of 2 minutes while type B showed a standard deviation of 4 minutes. Which of the two systems the bank should choose? (Points : 6)

System A because in shows more consistency in measuring the average waiting time.

System B because in shows more consistency in measuring the average waiting time.

Either because their mean waiting time is the same in both systems.

Neither because the given information is not enough to make a decision

10. (TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 40% red, 35% blue, 20% 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 $0, $5, $25, $70 for red, blue, yellow and green ball respectively.

Winning amount 0 5 25 70

Probability 40% 35% 20% 5%

(Points : 6)

The expected winning amount is $25.50

The expected winning amount is $14.50

The expected winning amount is $12.25

The expected winning amount is $10.25

11. (TCO 3) The grades of 20 students are listed below. Use the stem & leaf to determine the shape of the distribution. Choose the best answer.

4 | 4

5 | 6 8

6 | 5 7 9

7 | 1 5 7 8 8 9

8 | 3 4 5 7 8 8 9

9 | 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

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 20 students 8 of them are females. In how many ways can we select a group of 5 male students? (Points : 6)

56

792

6720

95040

15. (TCO 6) Research shows that the life time of Everlast automobile tires is normally distributed with a mean value of 70,000 miles and a standard deviation of 7,000 miles. What is the probability of having a tire that lasts more than 80,000 miles? (Points : 6)

0.9236

0.0778

0.0764

1.43

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 10 years experience and 14 years education level. (Points : 6)

52.2

72.5

70.5

91.5

17. (TCO 9) The estimated value for the correlation coefficient for this graph might be

(Points : 6)

-0.91

0.50

0.91

-0.50

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