Suppose that a recent poll found that 45% of adults in a certain country belief

Question

Suppose that a recent poll found that 45% of adults in a certain country belief that the overall state of moral values is poor. If a survey of a random sample of 20 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values.

Find and interpret the probability that exactly 11 of those surveyed feel the state of moral is poor?

Then find and interpret the probability that no more than 7 of those surveyed feel the state of moral is poor?

Then find and interpret the probability that more than 13 of those surveyed feel the state of moral is poor?

Find and interpret the probability that 9 or 10 believe the state of moral is poor?

Explanation / Answer

p = 0.45

n = 20

P(X = x) = 20Cx * 0.45x * (1 - 0.45)20-x

a) P(X = 11) = 20C11 * 0.4511 * 0.559 = 0.1185

B) P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

= 20C0 * 0.450 * 0.5520 + 20C1 * 0.451 * 0.5519 + 20C2 * 0.452 * 0.5518 + 20C3 * 0.453 * 0.5517 + 20C4 * 0.454 * 0.5516 + 20C5 * 0.455 * 0.5515 + 20C6 * 0.456 * 0.5514 + 20C7 * 0.457 * 0.5513

= 0.2520

c) P(X > 13) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)

= 20C14 * 0.4514 * 0.556 + 20C15 * 0.4515 * 0.555 + 20C16 * 0.4516 * 0.554 + 20C17 * 0.4517 * 0.553 + 20C18 * 0.4518 * 0.552 + 20C19 * 0.4519 * 0.551 + 20C20 * 0.4520 * 0.550

= 0.0214

d) P(9 or 10) = P(X = 9) + P(X = 10)

= 20C9 * 0.459 * 0.5511 + 20C10 * 0.4510 * 0.5510

= 0.1771 + 0.1593

= 0.3364

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