Business Statistics

Fall 2022 Midterm Exam

Question 1 (16pts)

Use the graph below to answer the questions below

a. Estimate the percentage of snow depth that were 240 cm or less

b. Estimate the minimum snow depth for the top 20% of the data

c. What are the minimum and maximum snow depth?

+

Question 2 (16pts)

The number of traffic citations issued last year by month in Beaufort County, South

Carolina is reported below

Citation by Month

January February March April May June July Aug Sept Oct Nov Dec

19 17 22 18 28 34 45 39 38 44 34 10

a. What is the mean number of citations?

b. Compute the sample standard deviation

c. What is the population variance of the citations?

d. Explain why the sample standard deviation is usually higher than the population

standard deviation.

e. Which measure of central tendency will be more appropriate for this data? Explain

Question 3 (16pts)

The data below represents the transport fares paid by 11 commuters

6 2 7 3 10 12 5 7 8 18 11

Determine the

a. 25th percentile

b. Median

c. Third Quartile

d. Interquartile range

Question 4 (16pts)

A survey asked 33,053 homeowners how many pets they owned. The results were as

followed:

Number of Pets Number of Homeowners

0 6464

1 9480

2 10,747

3 5017

4 or more 1345

Total 33,053

If a homeowner is randomly selected, determine the probability that he/she has

a. No pet

b. At most 2 pets

c. More than 3 pets

Question 5 (16pts

A poll was taken of 14,073 working adults aged 40-70 to determine their level of education.

The participants were classified by sex and by level of education. The results were as

follows.

Education Level Male Female Total

High School or Less 3310 2860 6170

Bachelor’s Degree 3067 3808 6875

Master’s Degree 506 422 928

Ph.D. 50 50 100

Total 6933 7140 14,073

If a person is selected at random. Compute the probability that the person

a. Is female

b. Is male or has a Ph.D.

c. Had masters degree given that he is male.

d. Is Female and has bachelors degree

Question 6 (20 pts)

It is estimated that 30% of households own a riding lawn mower. A sample of 30

households is selected and studied.

a. From this sample, how many are expected to own lawn mower?

b. What is the standard deviation of this distribution?

c. What is the probability that exactly 10 households own a riding lawn mower?

d. What is the probability that more than 10 of these own a riding lawn mower?

e. What is the probability that less than 15 of these own a riding lawn mower?