business statistics homework

DEC215 Business Statistics

Dr. A. Ampountolas Fall22

Assignment sheet 2

Due date: 18.11.2022 @ 11:59pm

Exercise 1.

The enrollments of the 13 public universities in the state of Ohio for the 2019-20

academic year are listed below.

College Enrollment

University of Akron 22,101 Bowling Green State University 19,423 Central State University 1,748 University of Cincinnati 44,969 Cleveland State University 16,667 Kent State University 39,598 Miami University 24,283 Ohio State University 67,524 Ohio University 36,287 Shawnee State University 3,600 University of Toledo 20,491 Wright State University 16,961 Youngstown State University 12,605

Questions:

1. Is this a sample or a population?

2. What is the mean enrollment?

3. What is the median enrollment?

4. Is there a mode for this distribution?

5. Would you select the mean or the median as most representative? Why?

6. What is the range of the enrollments?

7. Compute the standard deviation.

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Exercise 2.

Refer to the Valley Real Estate data (QM - Real Estate index.xlsx file) and prepare a

report on the sales prices of the homes. Be sure to answer the following questions in

your report.

Questions:

1. Around what values of price do the data tend to cluster? What is the mean sales

price? What is the median sales price? Is one measure more representative of the

typical sales prices than the others?

2. What is the range of sales prices? What is the standard deviation? About 95% of

the sales prices are between what two values? Is the standard deviation a useful

statistic for describing the dispersion of sales price?

3. Repeat parts (a) and (b) using FICO score.

Note: FICO refers to a credit score. Lenders use borrowers FICO scores along with

other details on borrowers credit reports to assess credit risk and determine whether to

extend credit.

Exercise 3.

Medical billing errors and fraud are on the rise. According to Medical Billing Advocates

of America, 8 out of 10 times, the medical bills that you get are not right. (”Services

Diagnose, Treat Medical Billing errors,”). If a sample of 10 medical bills is selected,

what is the binomial probability that:

Questions:

1. 0 medical bills will contain errors?

2. exactly 5 medical bills will contain errors?

3. more than 5 medical bills will contain errors?

4. What are the mean and standard deviation of the probability distribution?

Exercise 4.

The National Insurance Crime Bureau says that Miami- Dade, Broward, and Palm

Beach counties account for a substantial number of questionable insurance claims

referred to investigators. Assume that the number of questionable insurance claims

referred to investigators by Miami-Dade, Broward, and palm Beach counties is dis-

tributed as a poisson random variable with a mean of 10 per day.

Questions:

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1. What assumptions need to be made so that the number of questionable insurance

claims referred to investigators by Miami- Dade, Broward, and palm Beach

counties is distributed as a poisson random variable?

Making the assumptions given in (Q1), what is the probability that:

2. 5 questionable insurance claims will be referred to investigators by Miami-Dade,

Broward, and palm Beach counties in a day?

3. 10 or fewer questionable insurance claims will be referred to investigators by

Miami-Dade, Broward, and palm Beach counties in a day?

4. 11 or more questionable insurance claims will be referred to investigators by

Miami-Dade, Broward, and palm Beach counties in a day?

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Thank you!

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