A nationwide survey of college seniors by a university revealed that almost 70% disapprove daily pot smoking, according to a report in a magazine. If 14 seniors are selected at random and asked their opinion, find the probability that the number who disapprove of smoking pot daily is (a) anywhere from 7 to 9, (b) at most 5 and (c) not less than 8.

a) P ( 7 ≤ X ≤ 9) = 0.384

b) P(X ≤ 5) = 0.0083

c) P( X ≥ 8) = 0.904

Step-by-step explanation:

Proportion of college seniors that disapprove daily pot smoking, p = 0.7

Proportion of college seniors that do not disapprove daily pot smoking,

q = 1 - p = 1 - 0.7

q = 0.3

14 seniors are selected i.e. sample size, n = 14

This is a binomial distribution question:

a) probability that the number who disapprove of smoking pot daily is anywhere from 7 to 9

P ( 7 ≤ X ≤ 9) = P(X=7) + P(X=8) + P(X=9)

P ( 7 ≤ X ≤ 9) = P(X=7) + P(X=8) + P(X=9)

P ( 7 ≤ X ≤ 9) = 0.062 + 0.126 + 0.196

P ( 7 ≤ X ≤ 9) = 0.384

b) Probability that the number who disapprove of smoking pot daily is at most 5

P(X ≤ 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

P(X ≤ 5) = 0.0000000478 + 0.00000156 + 0.0000237 + 0.000221 + 0.00142 + 0.00662

P(X ≤ 5) = 0.0083

c) Probability that the number who disapprove of smoking pot daily is not less than 8.

P( X ≥ 8) = P(X=8) + P(X=9) + P(X=10) + P(X=11) + P(X=12) + P(X=13) + P(X=14)

P( X ≥ 8) = 0.126 + 0.194 + 0.229 + 0.194 + 0.113 + 0.041 + 0.00678

P( X ≥ 8) = 0.904