Estimate the probability of getting exactly 43 boys in 90 births. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
A) 0.0764
B) 0.0159
C) 0.0729
D) 0.1628

Question

Quizplus · Accepted Answer

The normal distribution is a good approximation to the binomial distribution when np and n(1-p) are both greater than or equal to 5. In this case, np = 90(0.5) = 45 and n(1-p) = 90(0.5) = 45, so the normal distribution is a good approximation.The mean of the binomial distribution is np = 45 and the standard deviation is sqrt(np(1-p)) = sqrt(45(0.5)(0.5)) = 4.95.The probability of getting exactly 43 boys in 90 births is the area under the normal distribution curve between z = (43 - 45) / 4.95 = -0.404 and z = (43 - 45) / 4.95 = 0.404. This area is approximately 0.0764.

Estimate the Probability of Getting Exactly 43 Boys in 90