Solution Found!
If Y has a geometric distribution with success probability
Chapter 3, Problem 76E(choose chapter or problem)
Of a population of consumers, 60% are reputed to prefer a particular brand, A, of toothpaste. If a group of randomly selected consumers is interviewed, what is the probability that exactly five people have to be interviewed to encounter the first consumer who prefers brand A? At least five people?
Questions & Answers
QUESTION:
Of a population of consumers, 60% are reputed to prefer a particular brand, A, of toothpaste. If a group of randomly selected consumers is interviewed, what is the probability that exactly five people have to be interviewed to encounter the first consumer who prefers brand A? At least five people?
ANSWER:Step 1 of 2
Given,
In a population, 60% are reputed to prefer particular brand A, of toothpaste.
The claim is to find the probability that exactly five people have to be interviewed to encounter the first consumer who prefers brand A and at least five people when a group of randomly selected consumers is interviewed
Where, p = 0.60 q = 1 - 0.6
= 0.4
We can use the Geometric distribution.
From the definition of Geometric distribution
\(\mathrm{P}(\mathrm{X})=p q^{x-1}, \mathrm{x}=0,1,2, \ldots \ldots\)