# MBA Level Statistics

See the attached files.

Have issues making sure these are correct. Must be answered in Excel.

1. A branch of chain of large electronics stores is conducting an end-of-month inventory of the merchandise in stock. There were 1546 items in inventory at that time. A sample of 50 items was randomly selected, and an audit was conducted, with the following results: X (mean) = $252.28, S = $93.67. Construct a 95% confidence interval estimate for the total value of the merchandise in inventory at the end of the month.

2. If the inspection division of a county weights and measures department wants to estimate the mean amount of soft-drink fill in 2-liter bottles to within +/- 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.05 liter, what sample size is needed?

3. In a recent year, about two-thirds of U.S. households purchased ground coffee. Consider the annual ground coffee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distributed as a normal random variable with a mean of $65.16 and a standard deviation of $10.00.

a. Find the probability that a household spent less than $35.00.

b. Find the probability that a household spent more than $60.00.

c. What proportion of the households spent between $40.00 and $50.00?

d. 99% of the households spent less than what amount?

4. The manager of the commercial mortgage department of a large band has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years (104 weeks) indicated the following:

Number of Commercial Mortgages Approved Frequency

0 13

1 25

2 32

3 17

4 9

5 6

6 1

7 1

a. Compute the expected number of mortgages approved per week.

b. Compute the standard deviation.

5. A bank branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1:00 p.m. lunch period. The waiting time, in minutes, is defined as the time the customer enters the line to when he or she reaches the teller window. Data are collected from a sample of 15 customers during this hour. See attachment.

a. Compute the mean and median

b. Compute the variance, standard deviation, range, coefficient of variation, and Z scores. Are there any outliers? Explain.

c. Are the data skewed? If so, how?

d. As a customer walks into the branch office during the lunch hour, she asks the branch manager how long she can expect to wait. The branch manager replies, "Almost certainly less than five minutes." On the basis of results of (a) through (c), evaluate the accuracy of this statement.

6. College football players trying out for the NFL are given the Wonderlic standardized intelligence test. The file Wonderlic - SEE ATTACHMENT, contains the average Wonderlic scores of football players at selected schools.

a. Construct a scatter plot with average Wonderlic score on the X axis and graduation rate on the Y axis.

b. What conclusions can you reach about the relationship between the average Wonderlic score and graduation rate?

7. See attachment STEEL. One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in an automobile. The steel is cut with a diamond saw and requires the resulting parts to be within +/- 0.005 inch of the length specified by the automobile company. Data are collected from a sample of 100 steel parts. The measurement reported is the difference in inches between the actual length of the steel part, as measured by a laser measurement device, and the specified length of the steel part. For example, the first value, -0.002, represents a steel part that is 0.002 inch shorter than the specified length.

a. Construct a frequency distribution and a percentage distribution.

b. Construct a cumulative percentage distribution.

c. Is the steel mill doing a good job meeting the requirements set by the automobile company? Explain.

#### Solution Summary

The solution discusses MBA level statistics.