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) 0.0159
B) 0.0764
C) 0.1628
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) for the binomial distribution. Here, n = 90 and p = 0.5 (assuming equal probability for boys and girls). Thus, μ = np = 45 and σ = √(np(1-p)) = √(90*0.5*0.5) = 4.743. Using the continuity correction, we find the z-score for 42.5 and 43.5, then calculate the probability between these z-scores using the standard normal distribution. The closest probability to the calculated value is 0.0764.

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