Question

6. A study from the Gallup Organization found that 45% of adult Americans believe that the overall state of the moral values in the US is poor. A study of 25 people is conducted. a. What is the probability that 15 or fewer of them think morals are poor? b. What is the probability that more than 17 of them think morals are poor? c. What is the probability that exactly 12 of them think morals are poor?

Answer 1

6. Let X be the random variable denoting the number of

American adults who believe that the overall state of the

moral values in the US is poor out of 25 adults.

Thus, X ~ Bin(25, 0.45)

a. The probability that 15 or fewer of them think morals are

poor = P(X <= 15) = = 0.9560. (Ans).

b. The probability that more than 17 of them think morals

are poor = P(X > 17) = P(X >= 18) = $\sum_{x = 18}^{25} \binom{25}{x} (0.45)^x(1-0.45)^{25 - x}$

= 0.0058. (Ans).

c. The probability that exactly 12 of them think morals are

poor = P(X = 12) = $\binom{25}{12} (0.45)^{12}(1-0.45)^{25 - 12}$ = 0.1511. (Ans).