A poll is given, showing 65% are in favor of

bobbie71G

bobbie71G

Answered question

2021-09-22

A poll is given, showing 65% are in favor of a new building project.
If 9 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?

Answer & Explanation

wheezym

wheezym

Skilled2021-09-23Added 103 answers

Step 1
Let X be the number of people who are in favor of a new building project which follows binomial distribution with sample size 9 and probability of success 0.65.
The binomial probability distribution is,
P(X=x)=(beg{array}{c}nxend{array})(p)x(1p)nx
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
Step 2
The probability that exactly 4 of them favor the new building project is,
P(X=4)=(beg{array}{c}94end{array})(0.65)4(10.65)94
=126×0.17850625×0.0052521875
=0.1181
Thus, the probability that exactly 4 of them favor the new building project is 0.1181.

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