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
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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