The average GPA for all college students is 2.95 with a standard deviation of 1.25.

Answer the following​ questions:

What is the average GPA for 50 MUW college​ students? (Round to two decimal​ places)

What is the standard deivaiton of 50 MUW college​ students? (Round to four decimal​ places)

A local statistician is interested in the proportion of high school students that drink coffee. Suppose that 20% of all high school students drink coffee. A sample of 75 high school students are asked if they drink coffee.

What is the probability that out of these 75 people, 14 or more drink coffee?

Random samples of students at 123 four-year colleges were interviewed several times since 1991. Of the students who reported drinking alcohol, the percentage who reported drinking daily was 32.2​% of 13,431 students in 1991 and 47.7% of 8507 students in 2003.

a. Estimate the difference between the proportions in 2003 and 1991​, and interpret.

b. Find the standard error for this difference.

c. Construct and interpret a 99​% confidence interval to estimate the true change.

d. State the assumptions for the confidence interval in​ (c) to be valid.

2. Student pricing at the movie theater is a common example of third degree price

discrimination. What is it about students, as compared to everyone else, that makes

movie theaters want or need to charge them a lower price? Why is it important for

movie theaters to make students show their IDs? Additionally, suppose a student could

buy as many tickets as they wanted with their ID. How might that limit the theater’s

ability to charge two drastically different prices for students and non-students?

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken.

a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? Explain the reason. Which theorem ensures the shape of the sampling distribution?

b. What is the probability that these 64 students will spend a combined total of more than $715.21?

c. What is the probability that these 64 students will spend a combined total between $703.59 and $728.45?

A researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playing the name game, the students were asked to recall as many first names of fellow students as possible. The mean number of names recalled was 19.41 with a standard deviation of 3.17. Use this information to solve the following problem.
What proportion of the students recalled less than 15 names?

a. .0823

b. .5823

c. .4177

d. .4923

The scores on an anthropology exam are normally distributed with a mean of 76 and a standard deviation of 5. Show your work step by step to receive full credit.

1) (6 points) The failing grade is anything 2.5 or more standard deviations below the mean. What is the cutoff for a failing score?

2) (6 points) If 3000 students took the exam, how many students failed? 3) (6 points) If 3000 students took the exam and the cutoff for an “A” grade is 90, how many students got an “A”?

A survey was conducted at two colleges. 500 students at College A participated in the study. The results indicated that on average, the students spent 15 hours per week doing online assignments and its standard deviation was 5 hours. At College B, 400 students participated in the study. The average hours they worked for online assignments was 20 with a standard deviation of 4 hours. Please test whether there is a true difference in the time students spent for online assignments between the two colleges (using a confidence level of 99%).

USING R : A random sample of 40 students took an SAT preparation course prior to taking the SAT. The sample mean of their quantitative SAT scores was 560 with a s.d. of 95, and the sample mean of their verbal SAT scores was 525 with a s.d. of 100. Suppose the mean scores for all students who took the SAT at that time was 535 for the quantitative and 512 for the verbal. Do the means for students who take this course differ from the corresponding means for all students at the 10% level of significance?