Consider the following to answer the question(s) below:
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) 50%

Question

Quizplus · Accepted Answer

We need to find the probability that a new machine set-up takes more than 30 minutes. We can standardize the value of 30 using the formula z = (x - μ)/σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

z = (30 - 22)/4 = 2

Looking at the z-table, we can see that the area to the right of 2 is 0.0228, which is equal to 2.28% (rounded to two decimal places). This means that only 2.28% of new machine set-ups take more than 30 minutes, so the answer is choice C, 2.28%.

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