At a local manufacturing plant, employees must complete new machine set ups within 30 Minutes.New machine set-up times can be described by a normal model with a mean of 22 Minutes and a standard deviation of four minutes.What percent of new machine set ups take More than 30 minutes?
A)97.72%
B)47.72%
C)2.28%
D)52.28%
E)none of the above

Question

Quizplus · Accepted Answer

To find the percentage of new machine setups that take more than 30 minutes, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (30 minutes), $\mu$ is the mean (22 minutes), and $\sigma$ is the standard deviation (4 minutes). Plugging in the values, we get $Z = \frac{30 - 22}{4} = 2$. Looking up a Z-score of 2 in a standard normal distribution table or using a calculator, we find that approximately 97.72% of values lie below a Z-score of 2, meaning 2.28% lie above it. Therefore, 2.28% of new machine setups take more than 30 minutes.

At a Local Manufacturing Plant, Employees Must Complete New Machine