Question

Suppose that a recent poll found that 40 % of adults in a certain country believe that the overall state of moral values is poor. If a survey of a random sample of 15 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values, complete parts (a) through (e) below.

(a) Find and interpret the probability that exactly

8 of those surveyed feel the state of morals is poor.

(b) Find and interpret the probability that no more than

3 of those surveyed feel the state of morals is poor.

(c) Find and interpret the probability that more than

9 of those surveyed feel the state of morals is poor.

(d) Find and interpret the probability that

6

or

7

believe the state of morals is poor.

(e) Would it be unusual to find

12

or more adults in the sample who believe the overall state of moral values is poor? Why?

Answer 1

Probability Mass Function of Binomial distribution is

Part a)

There is 11.81% of probability that exactly 8 out of 15 adults  in the country believe that the overall state of moral values is poor.

Part b)

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

P ( X <= 3 ) = 0.0905

There is 9.50% probability that no more than 3 adults  in the country believe that the overall state of moral values is poor.

Part c)

P ( X > 9 ) = P ( X = 10 ) + P ( X = 11 ) + P ( X = 12 ) + P ( X = 13 ) + P ( X = 14 ) + P ( X = 15 )

P ( X > 9 ) = 0.0338

There is 3.38% probability that more than 9 adults  in the country believe that the overall state of moral values is poor.

Part d)

P ( X = 6 ) + P ( X = 7 ) = 0.3837

There is 38.37% probability that 6 or 7 adults  in the country believe that the overall state of moral values is poor.

Part e)

P ( X >= 12 ) =  P ( X = 12 ) + P ( X = 13 ) + P ( X = 14 ) + P ( X = 15 )

P ( X >= 12 ) = 0.0019

Yes, it is unusual since the probability is less than 5% i.e < 0.05