Complete question is;
In a recent poll, the Gallup Organization found that 45% of adult Americans believe that the overall state of moral values in the United States is poor. Suppose a survey of a random sample of 25 adult Americans is conducted in which they are asked to disclose their feelings on the overall state of moral values in the United States. Find and interpret the probability that exactly 13 of those surveyed feel the state of morals is poor.
Answer:
P(X = 13) = 0.1236 or 12.36%
This means that in 100 trials, approximately 12 of the trials should have exactly 13 of those surveyed feel the state of morals is poor
Explanation:
We are given;
Sample size; n = 25
Chance of success; p = 45% = 0.45
This question is a binomial probability distribution problem and the formula is;
P(X = x) = nCx × p^(x) × (1 - p)^(n - x)
probability that exactly 13 of those surveyed feel the state of morals is poor is;
P(X = 13) = (25C13) × 0.45^(13) × (1 - 0.45)^(25 - 13)
P(X = 13) = 5200300 × 0.00003102864 × 0.00076621787
P(X = 13) = 0.1236 or 12.36%
This means that in 100 trials, approximately 12 of the trials should have exactly 13 of those surveyed feel the state of morals is poor