a. Construct an appropriate comparative graph for the heights of the members of the fencing teams.
b. Using your plot in part (a), describe the differences and similarities in the distributions of the
heights of the two teams.
- In the fictional story “The Legend of Sleepy Hollow,” the Headless Horseman chases Ichabod Crane
through the New England countryside. A video game based on this legend has Crane choosing his
route randomly, with a probability of 15% that he stays on the road and 85% that he cuts through the
forest. If he stays on the road, there is a 90% chance of the Horseman catching Ichabod. If he cuts
through the forest, there is only a 64% change of being caught. Find the probability that the next game
has Mr. Crane cut through the forest, given that the Horseman will indeed catch him.
- A local farmers’ market sells grapefruit and claims that the mass of these citrus fruits is
approximately normally distributed with a mean of 428.0 grams and a standard deviation of 21.1
grams. You purchase 10 grapefruit, and the average mass of these 10 fruits is 446.2 grams.
a. You wish to test the claim of the farmers’ market, so you begin by using a computer model to
simulate drawing 300 samples of size 10 from a population approximately N (428.0, 21.2) grams.
Above is the dotplot of the means from these 300 samples.
