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

Question

Quizplus · Accepted Answer

To use the normal approximation to the binomial distribution, we first calculate the mean (μ) and standard deviation (σ) of the binomial distribution. Here, n = 90 and p = 0.5 (assuming equal probability for boys and girls). Thus, μ = np = 45 and σ = sqrt(np(1-p)) = sqrt(22.5) ≈ 4.74. We then use the continuity correction for P(X = 43) by finding P(42.5 < X < 43.5). Converting to the standard normal distribution, we find the z-scores and calculate the probability, which is approximately 0.0764.

Estimate the Indicated Probability by Using the Normal Distribution as an Approximation