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A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30% of this population prefers the color green. If 18 buyers are randomly selected, what is the probability that at most 5 buyers would prefer green? Round your answer to four decimal places

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30% of this population prefers the color green. If 18 buyers are randomly selected, what is the probability that at most 5 buyers would prefer green? Round your answer to four decimal places

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 30% of this population prefers the color green. If 18 buyers are randomly selected, what is the probability that at most 5 buyers would prefer green? Round your answer to four decimal places.

Expert Solution
Step 1

Given that,

The random variable X is the color preferences of new car buyers.

30% population prefers green.

The probability of success is 0.30

The 18 buyers are randomly selected.

The buyers are selecting the color independently.

Therefore it is a binomial distribution.

X~B(n=18,p=0.30)

The p.m.f of the binomial distribution is as follows,

P(X=x)=Cxnpx(1-p)n-x      x=0,1,2...n=0                                  Otherwise

The combination is as follows,

Cxn=n!(n-x)!×x!

The factorial is as follows,

n!=n×(n-1)×...×1

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