Question

A process is normally distributed with a mean of 104 rotations per minute and a standard deviation of 8.2 rotations per minute. If a randomly selected minute has 118 rotations per minute, would the process be considered in control or out of control?A. In control as only one data point would be outside the allowable rangeB. In control as this one data point is not more than three standard deviations from the meanC. Out of control as this one data point is more than three standard deviations from the meanD. Out of control as this one data point is more than two standard deviations from the mean

Answer 1

Answer:

Option B) In control as this one data point is not more than three standard deviations from the mean

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 104 rotations per minute

Standard Deviation, σ = 8.2 rotations per

We are given that the distribution of process is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

For x = 118

$z = \displaystyle\frac{118-104}{8.2} = 1.7073$

Thus, we could say that this data point lies within three standard deviations from the mean as:

$\mu - 3\sigma < x < \mu + 3\sigma\\104-3(8.2) < x < 104 + 3(8.2)\\79.4 < 118 < 128.6$

Thus, it could be said

Option B) In control as this one data point is not more than three standard deviations from the mean