# Question

In basketball, when the probability of making a free throw is 0.50 and successive shots are independent, the probability distribution of the longest streak of shots made has μ = 4 for 25 shots, μ = 5 for 50 shots, μ = 6 for 100 shots, and μ = 7 for 200 shots.

a. How does the mean change for each doubling of the number of shots taken? Interpret.

b. What would you expect for the longest number of consecutive shots made in a sequence of (i) 400 shots and (ii) 3200 shots?

c. For a long sequence of shots, the probability distribution of the longest streak is approximately bell shaped and σ equals approximately 1.9, no matter how long the sequence (Schilling, 1990). Explain why the longest number of consecutive shots made has more than a 95% chance of falling within about 4 of its mean, whether we consider 400 shots, 3200 shots, or 1 million shots.

a. How does the mean change for each doubling of the number of shots taken? Interpret.

b. What would you expect for the longest number of consecutive shots made in a sequence of (i) 400 shots and (ii) 3200 shots?

c. For a long sequence of shots, the probability distribution of the longest streak is approximately bell shaped and σ equals approximately 1.9, no matter how long the sequence (Schilling, 1990). Explain why the longest number of consecutive shots made has more than a 95% chance of falling within about 4 of its mean, whether we consider 400 shots, 3200 shots, or 1 million shots.

## Answer to relevant Questions

For the Boston to Chicago route, an airline flies a Boeing 737–800 with 170 seats. Based on past experience, the airline finds that people who purchase a ticket for this flight have 0.80 probability of showing up for the ...Justify the px(1 - p)n-x part of the binomial formula for the probability P (x) of a particular sequence with x successes, using what you learned in Section 5.2 about probabilities for intersections of independent events. a. With random sampling, does the shape of the data distribution tend to resemble more closely the sampling distribution or the population distribution? Explain. b. Explain carefully the difference between a data ...Jan’s All You Can Eat Restaurant charges $8.95 per customer to eat at the restaurant. Restaurant management finds that its expense per customer, based on how much the customer eats and the expense of labor, has a ...According to a Boston Globe story, only about 1 in 6 Americans have blue eyes, whereas in 1900 about half had blue eyes. (Source: Data from The Boston Globe, October 17, 2006.) a. For a random sample of 100 living Americans, ...Post your question

0