At a cell phone assembly plant, 81% of the cell phone keypads pass inspection. A random sample of 97 keypads is analysed. Find the probability that more than 85% of the sample keypads pass inspection.
A)0.1587
B)0.8413
C)0.8577
D)0.1423

Question

Quizplus · Accepted Answer

The probability that more than 85% of the sample keypads pass inspection can be found using the normal approximation to the binomial distribution. The mean of the distribution is np = 97 * 0.81, and the standard deviation is sqrt(np(1-p)) = sqrt(97 * 0.81 * 0.19). To find the probability that more than 85% (or more than 82.45 keypads, since 85% of 97 is 82.45) pass inspection, we calculate the z-score for 82.45 and use the standard normal distribution to find the probability. The calculation shows that the probability is 0.1587, indicating that there is a 15.87% chance more than 85% of the sample keypads will pass inspection.

At a Cell Phone Assembly Plant, 81% of the Cell