Question

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

Answer 1

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) $P(X<3)=P(X=0)+P(X=1)+P(X=2)=$

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

$=0.0156+0.0938+0.2344=0.3438.$