13
RCMultiple Choice

Unit Test — Cumulative exam

Question 13 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

A racecar driver has a 0.05 probability of winning any given race in a season. There are 16 races in a season, and whether or not the driver wins one race is independent of whether he wins any other race. Let X represent the number of races the driver wins in the season.Have the conditions for a binomial setting been met for this scenario?

Answer
A
No, a sample size of 16 races is too small.
B
Yes, all four conditions in BINS have been met.
C
No, the probability of winning is too small for a binomial setting.
D
Yes, but they will only have been met if the racecar driver improves the probability of winning a race as the season progresses.

Explanation

A binomial setting requires a fixed number of trials, independent trials, two outcomes per trial, and the same probability of success on each trial. Here there are 16 races, each race is independent, the driver either wins or does not win, and the probability of winning stays 0.05. Therefore, all four BINS conditions are met, so the correct choice is “Yes, all four conditions in BINS have been met.”

AI-written and checked against the verified answer.

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