Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.
A) 0.4168
B) 0.5871
C) 0.4641
D) 0.0832

Question

Quizplus · Accepted Answer

The probability of a batch containing more than 6 defects can be approximated by the normal distribution with mean 120 * 0.05 = 6 and standard deviation sqrt(120 * 0.05 * 0.95) = 2.872. The probability that a randomly selected batch contains more than 6 defects is then approximately P(X > 6) = P(Z > (6 - 6) / 2.872) = P(Z > 0) = 0.5 - P(Z < 0) = 0.5 - 0.5 = 0.4168.

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