A recent article in the paper claims that government ethics are at an all-time low. Reporting on a recent sample, the paper claims that 31% of all constituents believe their representative possesses low ethical standards. Suppose 20 of a representative's constituents are randomly and independently sampled. Assuming the paper's claim is correct, find the probability that more than eight but fewer than 12 of the 20 constituents sampled believe their representative possesses low ethical standards.
A) 0.257174
B) 0.176107
C) 0.090085
D) 0.127128

Question

Quizplus · Accepted Answer

This is a binomial probability problem where n = 20 (number of trials), p = 0.31 (probability of success), and we are looking for the probability of getting more than 8 but fewer than 12 successes. Using the binomial probability formula or a calculator with binomial probability functions, we sum the probabilities of getting exactly 9, 10, and 11 successes. The correct sum of these probabilities is approximately 0.127128.

A Recent Article in the Paper Claims That Government Ethics