At a cell phone assembly plant, 79% of the cell phone keypads pass inspection. A random sample of 103 keypads is analyzed. Find the probability that more than 83% of the sample keypads pass Inspection.
A) 0.1251
B) 0.1587
C) 0.8749
D) 0.8413

Question

Quizplus · Accepted Answer

The sample size is larger than 30, so we can use the normal distribution to approximate the binomial distribution. 
The mean of the sample proportion is 0.79, and the standard deviation of the sample proportion is:
sqrt(0.79*0.21/103) = 0.046
To find the probability that more than 83% of the sample keypads pass inspection, we need to standardize the value:
z = (0.83 - 0.79)/0.046 = 0.87
Using a standard normal distribution table or calculator, we find that the probability of z being greater than 0.87 is 0.1587. Therefore, the answer is B.

At a Cell Phone Assembly Plant, 79% of the Cell