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Steve, Teacher

Category: Homework

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Experience: I teach Calculus and Probability in a University since 1994

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hello. i have several questions on stats and probability. they

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hello. i have several questions on stats and probability. they deal with hypothesis testing regarding a parameter, and estimating the value of the parameter. do you have time to do them or are you busy?

5 are multiple choice. But there's questions that have questions within them. Like theres question 1, then within question 1 there's question a, question b, etc.

1. what is the area under the standard normal curve that lies to the left of Z=0.95?

2. what is the area under the standard normal curve that lies to the right of Z= -1.26

3. what is the area under the standard normal curve between Z subscript 1=1.96 and Z subscript 2=-1.96

4. Find the Z-score such that the area under the standard normal curve to the left of the score is 0.5636.

5. determine Mu of x bar and sigma of x bar given the data below.

Mu=63, sigma=18, n=36

6. A simple random sample of size n is drawn from a population standard deviation is known to be 5.1. the sample mean, x bar, is determined to be 25.8

a. compute the 95% confidence interval about Mu if the sample size n=50

b. compute the 95% confidence interval about Mu if the sample size n=80

c. how does the sample size affect the margin of error?

A. as the sample size increases, the margin of error decreases

B. as the sample size increases, the margin of error stays the

same.

C. as the sample size decreases, the margin of error decreases.

d. compute a 99% confidence interval about Mu if the sample size n=50

e. how does the increasing the level of confidence affect the size of margin of error?

A. as the % confidence increases, the margin of error

increases

B. as the % confidence increases, margin of error stays the

same

C. as the % confidence decreases, margin of error increases

f. compare the 99% confidence interval to the 95% confidence interval.

A. as the % confidence increases, the size of the interval stays

the same

B. as the % confidence increases, the size of the interval

increases

C. as the % confidence decreases, size of the interval

increases

7. A random variable X is normally distributed with mu= 20 and sigma=4.

a. compute (z subscript 1= x subscript 1 – mu divided by

sigma) for x subscript 1=14

b. compute (z subscript 2= x subscript 2 – mu divided by

sigma) for x subscript 2=21

c. the area under the normal curve between x subscript 1=14

and x subscript 2=21 is 0.5319. what is the area between Z’s

of 1 and Z’s of 2.

8. assume that the random variable X is normally distributed with a mean of mu=48 and a standard deviation of sigma=6

what is P(38<X<68)?

9. sketch and label a normal curve for the data in #8.

10. the number of peppermints in a 1 pound bag of the candy is normally distributed with a mean of 75 and a standard deviation of 9 candies.

a. whats the probability that a randomly selected bag contains

fewer than 65 peppermints?

b. whats the probability that a randomly selected bag contains

between 60 and 85?

c. what proportion of bags contains more than 70 peppermints?

11. the amount of time adults spend online is closely monitored by firms because this helps to determine ad costs.

a. do YOU THINK the variable “daily time spent online” would

be normally distributed, yes or no?

b. if you chose “no” for part a, what shape would you expect

the variable to have?

A. skewed left

B. skewed right

C. symmetric

D. uniform

Continuation of #11: further, this survey tells us that adults spend 1.75 hours/day online on a weekday. Assume that the standard deviation for “daily time spent online” is 0.75 hours. If a random sample of n=50 adults is obtained, describe the sampling distribution of x bar, the mean amount of daily spent online.

For the continuation, x bar is approximately normal with Mu of x bar= , and sigma of x bar= .

12. use the data in #11 to complete this problem.

Determine the probability that a random sample of 50 adults results in a mean “daily time spent online” of between 1.5 and 2 hours.

13. According to a study conducted by a statistical organization, the proportion of americans who are satisfied with the way things are going in their lives is 0.92. suppose that a random sample of 100 americans is obtained.

a. describe the sampling distribution of p hat. Choose the

correct answer.

A.distribution of p hat is approximately normal with(Mu

of p hat=0.92 and sigma of p hat=0.027)

B. distribution of p hat is approximately normal with (Mu

of p hat=0.92 and sigma of p hat=0.054)

C. distribution of p hat is binomial with n=100 and p=0.92

D. Distribution of p hat is uniform.

b. what is the probability that at least 85 americans in the sample are

satisfied with their lives?

c. whats the probability that 90 or fewer americans in the sample are

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