Question

A process is normally distributed with a mean of 10.2 hits per minute and a standard deviation of 1.04 hits. If a randomly selected minute has 13.9 hits, would the process be considered in control or out of control?

(a) In control as this one data point is not more than three standard deviations from the mean.
(b) Out of control as this one data point is more than two standard deviations from the mean.
(c) In control as only one data point would be outside the allowable range.
(d) Out of control as this one data point is more than three standard deviations from the mean.

Answer 1

The correct answer is option d. The process is considered out of control because a randomly selected minute with 13.9 hits is more than three standard deviations from the mean, following the Empirical Rule for a normally distributed process.

Step-by-step explanation:

When evaluating whether a process is in control or out of control, one must consider the position of data points relative to the mean and standard deviations. According to the Empirical Rule, approximately 68% of data is within one standard deviation from the mean, about 95% within two standard deviations, and over 99% within three standard deviations for a bell-shaped distribution.

In this case, the process has a mean of 10.2 hits per minute and a standard deviation of 1.04 hits. A randomly selected minute producing 13.9 hits can be analyzed by calculating the number of standard deviations away from the mean this value is:

Z = (X - μ) / σ = (13.9 - 10.2) / 1.04 ≈ 3.56.

This value is more than three standard deviations from the mean, leading to the conclusion that the process is out of control as per option (d).