Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.
A) 0.0769
B) 0.0669
C) 0.0679
D) 0.9331

Question

Quizplus · Accepted Answer

To use the normal approximation, calculate the mean (np) and standard deviation (sqrt(np(1-p))) for the binomial distribution. Here, n=140 and p=0.7, so mean = 98 and standard deviation ≈ 5.42. Use the continuity correction for P(X=100) as P(99.5 < X < 100.5) and find the z-scores. The probability corresponds to choice B.

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