Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.
A)0.0065
B)0.0051
C)0.0057
D)0.0034

Question

Quizplus · Accepted Answer

Using the normal approximation to the binomial distribution, we calculate the mean (np) and standard deviation (sqrt(np(1-p))) for n=10,000 and p=0.02. The mean is 200, and the standard deviation is approximately 14. The z-score for 225 is (225-200)/14 ≈ 1.79. Using the standard normal distribution table, the probability corresponding to this z-score is approximately 0.0057.

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