1. (Section 8.1) The exam scores for a math exam given at a university are normally distributed with a mean of 72 and a standard deviation of 8. Suppose a random sample of 20 students is selected from all students that took the exam.

a) Determine the shape of the distribution for the sample mean, $\overline{x}$.

A) Normal, since the sample size is at least 30.

B) Normal, since the population is normal.

C) Uniform, since the average is always the same.

D) Not enough information is given

b) Determine the mean of the distribution for the sample mean, $\overline{x}$, rounded to the nearest whole number.

c) Determine the standard deviation of the distribution for the sample mean, $\overline{x}$, rounded to 3 decimal places.

d) Find the probability that a single student scores at least 76 on the exam, rounded to 3 decimal places.

e) Find the probability that the sample of 20 students has a mean score of at least 76, rounded to 3 decimal places.

2.(Section 8.2) The percentage of college students that change their majors before graduating is (approximately) 80%. A random sample of 500 graduating college students is obtained, and the sample proportion,

$\hat{p}$, is the proportion of the sample that changed their majors.

a) Determine the shape of the distribution for the sample proportion, $\hat{p}$(single letter answer only).

A) Normal, since $n\cdot p\cdot (1-p)\ge 10$.

B) Normal, since the sample size is at least 30.

C) Uniform, since the percentage is always 80%.

D) Not enough information is given

b) Determine the mean of the distribution for the sample proportion, $\hat{p}$, rounded to the nearest whole number.

c) Determine the standard deviation of the distribution for the sample proportion, $\hat{p}$, rounded to 3 decimal places.

d) Find the probability that at least 420 students changed their majors using normalcdf, rounded to 3 decimal places.

e) Find the probability that less than 77% of students changed their majors using normalcdf, rounded to 3 decimal places.

3.(Section 9.1) In a random sample of 250 college students, 213 said that they enjoyed reading for fun. Construct a 95% confidence interval for the proportion of college students that enjoy reading for fun. Then find each of the following, rounded to 3 decimal places.

Lower Bound =

Upper Bound =

Point Estimate =

Margin of Error =

4.(Section 9.1) Using sample data for 350 students, a researcher, Max, determines that a 95% confidence interval for the proportion of college students that play video games regularly is (0.691, 0.713). Interpret the confidence interval in a complete sentence.

5.(Section 9.1) A researcher, Tate, wants to get a fairly accurate estimate for the proportion of students that experience high test anxiety. First, Tate needs to determine the number of students needed for a sample in order to estimate the proportion within 1%. Moreover, Tate wishes to use a 99% level of confidence.

a) Find the number of students needed for the sample (without any other information).

b) Find the number of students needed if Tate found a previous estimate that 15% of students experience high test anxiety.