the measures should be reduced (subtracted) by 0.5 bushels. Describe the impact doing so would
have on the mean, median, standard deviation, and interquartile range of the treatment group.
- A particular bottle-filling machine is supposed to put 16 ounces of water into a bottle. The amount
actually dispensed is approximately normal with mean 16.1 ounces and a standard deviation of 0.12
ounces. A bottle is rejected by quality control if it contains less than 15.7 ounces or more than 16.3
ounces.
a. What is the probability that a randomly selected bottle gets rejected by quality control?
b. What is the probability that, out of 20 randomly selected bottles, at least 2 are rejected by quality
control?
c. What is the probability that a set of 5 randomly selected bottles contains, on average, more than
16.2 ounces of water?
- A student was curious about a news article that reported the percentage of Americans who believe
that a “higher power” affects who wins sporting events. With the assumption that the percentage
reported in the article is correct, she simulated selecting samples of 100 Americans and calculating
the percentage of those that believe a higher power has a hand in who wins a sporting event. The
results of 200 trials are shown below.
a. Based on the results of these trials, what appears to be the reported percentage of Americans that
believes the results of a sporting event are influenced by a “higher power?” Explain.
b. Another student believes that the proportion reported in the article is too low. He takes a random
sample of 100 Americans and finds that 44 percent believe in the influence of a “higher power”
on the outcome of a sporting event. Based on the dotplot above, does it appear the percentage in
the article is correct? Explain why or why not.
- Below are the residual plots generated for the linear regression on three separate sets of bivariate
data.
