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)0.4641
C)0.5871
D)0.0832

Question

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)0.4641
C)0.5871
D)0.0832

Quizplus · Accepted Answer

The probability of a batch containing more than 6 defects is the same as the probability of a batch containing 7 or more defects. The mean of the binomial distribution is np = 120 * 0.05 = 6, and the standard deviation is sqrt(np(1-p)) = sqrt(6 * 0.95) = 2.45. The probability of a batch containing 7 or more defects is the same as the probability of a z-score greater than (7 - 6) / 2.45 = 0.41. The probability of a z-score greater than 0.41 is 0.3413, so the probability of a batch containing 7 or more defects is 0.3413.

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