A research study relative to home values was conducted in a medium-sized city in Utah. A random sample of 183 home values was evaluated over a five-year period. It was found that home values had steadily decreased during this time. Which of the following accurately describes the relationship between the mean and median?
The median value was greater than the mean.
The median value was less than the mean.
The median value and the mean were approximately equal.
Concept: Box-plot diagram analysis of multiple data sets using the same scale.
The table below documents the 5-number summary of the egg length in millimeters (mm) of three different wild bird species. Use this data to create a box plot diagram, then answer the question that follows.
Bird #1
Bird #2
Bird #3
Lowest Value
21.0
20.8
21.0
Q1
22.5
22.7
22.0
Median
23.3
23.0
23.0
Q3
23.8
23.8
24.0
Highest Value
24.0
25.0
24.8
Using the box-plot diagram to compare the lengths of the eggs of the three bird species, indicate which interpretation you feel is NOT correct.
The median lengths of the eggs of the three wild bird species are about the same.
The distribution of the length of the eggs is roughly symmetric for Bird #2 and Bird #3, while it was right skewed for Bird #1.
The variation in length of eggs was greatest in Bird #2 and least in Bird #3.
A comparative box-plot diagram is a good method of comparing the egg length of these three bird species.
Concept: Analysis of the probability of “at least one” event occurring
You have applied for a statistical research position at two research firms, Lighthouse Research and Analytical Data Services. The probability of getting an offer from Lighthouse Research is 0.6, and the probability of getting an offer from Analytical Data Services is 0.3. Assuming that the two job offers are independent of each other, what is the probability that you will get at least one offer?
0.72
0.90
0.28
0.18
Concept: Analysis of conditional probability
The Board of Directors of Williams Valve Company has made the following estimates for the upcoming year’s annual earnings:
P(earnings lower than this year) = .30
P(earnings about the same as this year) = .50
P(earnings higher than this year) = .20
After talking with union leaders, the human resource department has drawn the following conclusions:
P(Union will request wage increase | lower earnings next year) = .25
P(Union will request wage increase | same earnings next year) = .40
P(Union will request wage increase | higher earnings next year) = .90
Calculate the probability that the company has higher earnings next year and the union does not request a wage increase.
.20
.18
.90
.02
Concept: Analysis of expected values
A local ski resort loses $100,000 per season when it does not snow very much. The resort breaks even during an average snowfall year and makes $250,000 in years when the snow base exceeds 80 inches (a good snow year). The probabilities of these three snow year events is 0.20 (bad year), 0.45 (average year) and 0.35 (good year).
Would you invest $70,000 to receive a payment of the expected value?
No. The expected value is less than my investment.
No. The expected value is the break even amount.
Yes. The expected value is less than my investment, but the chance to make $180,000 is reasonable.
Yes. The expected value is greater than my investment.
Concept: Analysis of a situation utilizing the binomial probability distribution.
Natural gas leak detection systems are designed to detect and warn of natural gas leaking from the cylinder. A reliability question is whether a detection system will be able to identify leaks and issue a warning. Assume that a particular detection system has a .90 probability of detecting a leak. A statistician used the binomial probability distribution to answer the following questions, obtaining the answers shown.
Question 1: What is the probability that a single detection system will detect a leak? Answer: 90%
Question 2: If two detection systems are installed and operated independently, what is the probability that at least one of the systems will detect a leak? Answer: 99%
Question 3: If three detection systems are installed and operated independently, what is the probability that at least one of the systems will detect a leak? Answer: 99.9%
Would you recommend that multiple detection systems be used?
No, because the number of detection systems used is not related to cylinder leakage.
Yes, because it is almost certain that the leak will be detected if three systems are installed.
Yes, because there is less than a one thousandth chance that a cylinder will leak.
No, because there is a 90% chance that the leak will be detected.
Concept: Analysis of computing probabilities and x values for the normal distribution.
Sample Solution
