Question

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities. Fifty dash seven percent of adults say that they have cheated on a test or exam before. You randomly select eight adults. Find the probability that the number of adults who say that they have cheated on a test or exam before is​ (a) exactly four​, ​(b) more than two​, and​ (c) at most five.

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

Sample size, n = 8

P(a person have cheated), p = 0.57

q = 1 - p = 0.43

a) P(exactly four), P(4) = 8C4x0.57⁴x0.43⁴

= 0.2526

b) P(more than two), P(X > 2) = 1 - [P(0) + P(1) + P(2)]

= 1 - [0.43⁸ + 8x0.57x0.43⁷ + 8C2x0.57²x0.43⁶]

= 0.9289

c) P(at most 5) = 1 - [P(6) + P(7) + P(8)]

= 1 - [8C6x0.57⁶x0.43² + 8x0.57⁷x0.43 + 0.57⁸]

= 0.7440