Poisson Distribution (Optional) · Exercise 23

Approximately 8 percent of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number who participated in after-school sports all four years of high school.

(a) In words, define the random variable X.
(b) List the values that X may take on.
(c) Give the distribution of X. X ~ _____(_____,_____)
(d) How many seniors are expected to have participated in after-school sports all four years of high school?
(e) Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.
(f) Based on numerical values, is it more likely that four or that five of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §4.6 Poisson Distribution (Optional) · Exercise 23