In a recent poll, 44 % of survey respondents said that, if they only had one child, they would prefer the child to be a boy. Suppose you conducted a survey of 150 randomly selected students on your campus and find that 71 of them would prefer a boy.

(a) Use the normal approximation to the binomial to approximate the probability that, in a random sample of 150 students, at least 71 would prefer a boy, assuming the true percentage is 44 %.

(b) Does this result contradict the poll? Explain.

Question

Jon Frazier

Mathematics

4 June, 01:49

In a recent poll, 44 % of survey respondents said that, if they only had one child, they would prefer the child to be a boy. Suppose you conducted a survey of 150 randomly selected students on your campus and find that 71 of them would prefer a boy.

(a) Use the normal approximation to the binomial to approximate the probability that, in a random sample of 150 students, at least 71 would prefer a boy, assuming the true percentage is 44 %.

(b) Does this result contradict the poll? Explain.

+3

Answers (1)

Know the Answer?

Nicholas Becker · Answer 1

a) The probability that 71 of 150 will prefer boy child is 71/150 or 0.47

b) The result contradicts the poll actual percentage is 47.33% which is 3.33% more than the poll predicted

Step-by-step explanation:

If 71 out of 150 prefer boy child

The probability that the 71 will prefer boy child is

= 71/150

The actual percentage is

(71/150) * 100%

= 47.33%

This contradicts the poll as this is more than the poll predicted. That means Less than 71 of 150 actually preferred boy child.