Answer to Question #130349 in Mechanical Engineering for Kenneth

Question

A nationwide survey of 20,000 students by the university revealed that almost 78% disapprove of smoking. If 15 of these seniors are selected at random and asked their opinions are selected at random and asked their opinions, what is the probability that more than 11 but less than 14 disapprove of smoking? *

Answer 1

Using binomial distribution

Let A be an event of disapproval of smoking by student during trial.

Probability of event of disapproval of smoking=P(A)=p=78%=0.78

Probability of event of approval of smoking =q=1-p=0.22

When 15 seniors are selected at random, N=15.

then, the probability that more than 11 but less than 14 disapprove of smoking is given by,

P(11<X<14)=P(X=12)+P(X=13)

The probability that more than 11 but less than 14 disapprove of smoking is given by,

P(11<X<14)=0.2457+0.20103=0.4467