Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-Two percent of hair dryers produced at a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, the number of defectives is between 195 and 210 inclusive.
A)0.4251
B)0.4034
C)0.4017
D)0.3989

Question

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-Two percent of hair dryers produced at a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, the number of defectives is between 195 and 210 inclusive. 
A)0.4251
B)0.4034
C)0.4017
D)0.3989

Quizplus · Accepted Answer

The normal distribution is a good approximation to the binomial distribution when np and n(1-p) are both at least 5. In this case, np = 10,000 * 0.02 = 200 and n(1-p) = 10,000 * 0.98 = 9800, so the normal distribution is a good approximation.The mean of the binomial distribution is np = 200 and the standard deviation is sqrt(np(1-p)) = sqrt(200 * 0.98) = 14.0.The probability that the number of defectives is between 195 and 210 inclusive is the area under the normal curve between z = (195 - 200) / 14 = -0.36 and z = (210 - 200) / 14 = 0.71. This area is approximately 0.4034.

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