According to a survey in a country, 37% of adults do not have any credit cards.

Question

According to a survey in a country, 37% of adults do not have any credit cards. Suppose a simple random sample of 800 adults is obtained. Would it be unusual if a random sample of 800 adults results in 312 or more having no credit cards?

A. The result is not unusual because the probability that ^p is greater than or equal to its sample proportion is less than 5%.

B. The result is unusual because the probability that ^p is greater than or equal to this sample proportion is greater than 5%.

C. The result is not unusual because the probability that ^p is greater than or equal to this sample proportion is greater than 5%.

D. The result is unusual because the probability that ^p is greater than or equal to this sample proportion is less than 5%.

Explanation / Answer

mean=n*p=800*0.37 =296

standard deviation =sqrt(n*p*(1-p))

=sqrt(800*0.37*(1-0.37))

=13.65577

So the probability is

P(X>=312) = P((X-mean)/s >(312-296)/13.65577)

=P(Z>1.17) = 0.1210 (from standard normal table)

Answer: C. The result is not unusual because the probability that ^p is greater than or equal to this sample proportion is greater than 5%.

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