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 = (X - μ) / σ, where X is the value of interest (30 minutes), μ is the mean (22 minutes), and σ is the standard deviation (4 minutes). Plugging in the values, we get Z = (30 - 22) / 4 = 8 / 4 = 2. A Z-score of 2 corresponds to a percentile of approximately 97.72% in a standard normal distribution, meaning 97.72% of values lie below 30 minutes. Therefore, 100% - 97.72% = 2.28% of new machine setups take more than 30 minutes.

At a Local Manufacturing Plant, Employees Must Complete New Machine