Description
Complete the problems below from the textbook. You will need to use the "Buena School District Bus Data" and the "Century National Bank Data" files for this assignment.
- Chapter 8 – Problem 44
- Chapter 8 – Problem 48
- Chapter 9 – Problem 56
- Chapter 9 – Problem 66
- Chapter 9 – Problem 71
- Chapter 9 Case A – Century National Bank
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Running head: BUSINESS STATISTICS PROBLEMS
Business Statistics Problems
Student’s Name
Professor’s Name
Course Title
Date
BUSINESS STATISTICS PROBLEMS
44. An economist uses the price of a gallon of milk as a measure of inflation. She finds that
the average price is $3.50 per gallon and the population standard deviation is $0.33. You
decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute
the mean price for the sample.
a. What is the standard error of the mean in this experiment?
Standard error = δ / √n
0.33/√40 = 0.052178
b. What is the probability that the sample mean is between $3.46 and $3.54?
µ = 3.50
δ = 0.33
x1 = 3.46
x2 = 3.54
Z = (xi - µ)/δ
Z3.46 = (3.46 – 3.50)/0.33 = -0.1212
Z3.54 = (3.54 – 3.50)/0.33 = 0.1212
P (3.46 ≤ x ≤ 3.54) = P(-0.1212 ≤ Z ≤ 0.1212)
0.0478 + 0.0478 = 0.0956
P = 9.56%
It is very unlikely that a sample mean is between $3.46 and $3.54.
c. What is the probability that the difference between the sample mean and the population
mean is less than $0.01?
2
BUSINESS STATISTICS PROBLEMS
P (xs – xp) ˂ 1
P(x-bar > 3.08) = P(z > 2.8070) = normalcdf(2.8070,100) = 0.0025
d. What is the likelihood the sample mean is greater than $3.60?
Z = (3.60 – 3.50)/0.33 = 0.3030
P (x ≥ 3.60) = P (Z ≥ 0.3030)
0.5 -0.6179 = - 0.1179
= 11.79%
48. Refer to the Buena School District bus data. Information provided by manufacturers of
school buses suggests the mean maintenance cost per month is $455 per bus. Use statistical
software to find the mean and the standard deviation for the Buena buses. Does the
Buena data seem to be in line with that reported by the manufacturer? Specifically, what is
the probability of the sample mean being less than Buena’s, given the manufacturer’s data?
The calculated sample mean maintenance cost per month of the Buena buses is $450.29 while
the standard deviation is $53.69.
According to the information provided by the manufacturer, the mean maintenance cost per
month is $455 per bus.
3
BUSINESS STATISTICS PROBLEMS
4
The Buena data is in line with that reported by the manufacturer given that it falls within the 95%
confidence interval: 438.52 ≤ x ≤ 462.05
Z = (455 – 450.29)/53.69 = 0.0877
P (x ≤ 455) = P (Z ≤ 0.0877)
0.5 – 0.5359 = - 0.0359
= 0.4641
P = 46%
CH.9
55. You are to conduct a sample survey to determine the mean fami...
