Each evening, a nationwide retail chain randomly calls 100 of the customers who came to their store that day to ask whether they were satisfied with the service they had received. The customers respond yes or no. Suppose the company has found over time that 8 percent of the customers are not satisfied ("no" answers), what is the 3-sigma upper and lower control limits for the appropriate control chart?
A) About .053 and .107
B) 0 to about .16
C) -.0.14 to about .16
D) About -1.96 to 1.96

Question

Quizplus · Accepted Answer

The control limits can be calculated using the formula for the binomial distribution's standard deviation, $\sigma = \sqrt{np(1-p)}$, where $n$ is the sample size (100) and $p$ is the probability of a "no" answer (0.08). The 3-sigma control limits are calculated as $p \pm 3\sigma$. Given $p = 0.08$, the calculation yields control limits that are approximately 0 (since the number of dissatisfied customers cannot be negative) and about 0.16.

Each Evening, a Nationwide Retail Chain Randomly Calls 100 of the Customers