MATH 533 HK Statistics Ages of College Professors Questions

Statistics Exam 2 Spring 2023
Name:______________________________________
Download the Exam 2 file to your computer and print it out. Write out all of your work to each problem on the hard
copy of the exam. The completed exam must be sent in pdf or jpeg format, and it must be sent via the submission
tool in Vancko Hall ABSOLUTELY NO LATE SUBMISSIONS WILL BE ACCEPTED!
1. Ages of college professors are normally distributed with a mean of 50 years and a standard deviation of 2 years .
Use the EMPIRICAL RULE to answer the following questions. DO NOT USE TABLE E TO ANSWER THESE
QUESTIONS. Please show any important calculations and do not round any numbers off. (part a worth 10 pts,
parts b-e worth 6 pts each)
a.
Draw the normal curve below, labeling it as we did in class.
b. What age cuts off the oldest 2.5% of professors? Box in final answer please.
c. What age cuts off the youngest 16% of professors? Box in final answer please.
d. What percent of professors are less than 46 years old? Box in final answer please.
e. What percent of professors are older than 52 years old? Box in final answer please.
2. The time is takes to play a Monopoly game is normally distributed and has a mean of 89.5 minutes and a
standard deviation of 11.2 minutes . Use this information to answer parts a % below. Include a diagram for
each problem, clearly showing the appropriate shading. For each problem, you must show your work by hand
and then check the answer on the graphing calculator. Put final answers in each box. REPORT FINAL ANSWERS
TO 4 DECIMALS
a. What is the probability that a randomly chosen Monopoly game lasted longer than 70 minutes?
Answer obtained by hand:
Answer obtained from graphing calculator:
b. What is the probability that a randomly chosen Monopoly game lasted between 85 minutes and 100
minutes?
Answer obtained by hand:
Answer obtained from graphing calculator:
c. What is the probability that a randomly chosen SAMPLE of 10 Monopoly games lasted an average less than 95
minutes?
Answer obtained from graphing calculator:
d. . If in part c, if a sample of 25 Monopoly games was chosen instead of a sample of 10, would the standard
deviation increase, decrease, or stay the same? Explain your reasoning please.
e. Find the time that cuts off the top 15% of the data. Report your final answers to two decimal places.
Answer obtained by hand:
Note: #2a, b, c, e worth 15 pts each; #2d worth 6 pts
Answer obtained from graphing calculator:

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