# Normal Distribution

1. Using the MM207   Student Data Set:

a) What is the correlation between   student cumulative GPA and the number of hours spent on school work each week? Be sure to include the computations or StatCrunch output to support   your answer.

b) Is the correlation what you expected?

c) Does the number of hours spent on   school work have a causal relationship with the GPA?

d) What would be the predicted GPA for a student who spends 16 hours per week on school work?.

2. Using the MM207   Student Data Set:

a) Select a continuous variable that you   suspect would not follow a normal distribution.

b) Create a graph for the variable you have selected to show its distribution.

c) Explain why these data might not be normally distributed.

d) Select a second continuous variable that you believe would approximate a normal distribution

e) Create a graph to show its distribution.

f) Explain why these data might be normally distributed.

3. Jonathan is a 42 year old male student and Mary is a 37 year old female student thinking about taking this class. Based on their relative position, which student would be farther away from the average age of their gender group based on this sample of MM207 students?

4. If you were to randomly select a student from the set of students who have completed the survey, what is the probability that you would select a male? Explain your answer.

5. Using   the sample of MM207 students:

a) What is the probability of   randomly selecting a person who is conservative and then selecting from that   group someone who is a nursing major?

b) What is the probability of   randomly selecting a liberal or a male?

6.   Facebook reports that the average number of Facebook friends worldwide is 175.5 with a standard deviation of 90.57. If you were to take a sample of 25 students, what is the probability that the mean number Facebook friends in the sample will be 190 friends or more?

7. Select a random sample of 30 student responses to question 6, “How many credit hours are you taking this term?” Using the information from this sample, and assuming that our data set is a random sample of all the statistics students, estimate the average number of credit hours that all the statistics students are taking this term using a 95% level of confidence. Be sure to show the data from your sample and the data to support your estimate.

8. Assume that the MM207 Student Data Set is a random sample of all the students; estimate the proportion of all the students who are male using a 90% level of confidence.

9. Assume you want to estimate with the proportion of students who commute less than 5 miles to work within 2%, what sample size would you need?

10. A professor at the University claims that the average age of all the students is 36 years old. Use a 95% confidence interval to test the professor’s claim. Is the professor’s claim reasonable or not? Explain.

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