Answer to Question #196091 in Statistics and Probability for Julia

Question

Suppose that a salesperson succeeds in making a sale with three in every 4 potential customers contacted. a particular week 5 new potential customers are conducted.

What is the probability read the salesperson will succeed in making at least 4 sales?

Answer 1

$P=\dfrac{3}{4}=0.75$

Given distribution is a binomial distribution

$X\sim bin(5,0.75)$

 Probability that the salesperson will succeed in making at least 4 sales-

$P(X\ge 4)=1-P(X>4)$

$\\=1-P(X=5)\\[9pt]=1-^5C_5(0.75)^5(0.25)^0\\[9pt]=1-0.2373=0.7626$