find and interpret the probability that no more than 10 of those surveyed feel t

Question

find and interpret the probability that no more than 10 of those surveyed feel the state of morals is poor. 36. Morality In a recent poll, the Gallup Organization found that45% 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 (a) Find and interpret the probability that exactly 15 of those surveyed feel the state of morals is poor. (b) Find and interpret the probability that no more than 10 of those surveyed feel the state of morals is poor.

Explanation / Answer

Solution:-

p = 45/100

p = 0.45

n = 25

a) The probability that exactly 15 of those surveyed feel the state of morals is poor is 0.05202.

x = 15

By applying binomial distribution:-

P(x, n) = nCxpx*(1-p)(n-x)

P(x = 15) = 0.05202

b) The probability that no more than 10 of those surveyed feel the state of morals is poor is 0.3843.

x = 10

By applying binomial distribution:-

P(x, n) = nCxpx*(1-p)(n-x)

P(x < 10) = 0.3843

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