Answer to Question #188503 in Statistics and Probability for LE6

Question #188503

In a survey, one-half of Demacia's universities give their employees 4 weeks of vacation after they have been with the company for 15 years. Find the probability that among 6 companies surveyed at random, the number that give employees that said benefit is,

a) anywhere from 2 to 5

b) fewer than 3


answers must be in decimal format and must have four decimal places.

a) P(2 ≤ X ≤ 5) = Blank 1

b) P(X < 3) = Blank 2

1
Expert's answer
2021-05-07T13:09:47-0400

This is a binomial distribution with p=0.5, n=6.


a) "P(2\\le X\\le 5)=P(X=2)+P(X=3)+P(X=4)+P(X=5)="

"=C_6^20.5^20.5^4+C_6^30.5^30.5^3+C_6^40.5^40.5^2+C_6^50.5^50.5^1="

"=0.2344+0.3125+0.2344+0.0938=0.875."


b) "P(X<3)=P(X=0)+P(X=1)+P(X=2)="

"=C_6^00.5^00.5^6+C_6^10.5^10.5^5+C_6^20.5^20.5^4="

"=0.0156+0.0938+0.2344=0.3438."


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