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.
-The typical worker needs five minutes to adjust to their surroundings before beginning their duties. What percent of new machine set-ups are completed within 25 minutes to allow for this?
A) 77.3%
B) 27.3%
C) 22.7%
D) 72.7%
E) 0.75%

Question

Quizplus · Accepted Answer

To find the percent of new machine set-ups completed within 25 minutes, we need to use the Z-score formula:

Z = (X - μ) / σ

where X is the time (25 minutes), μ is the mean (22 minutes), and σ is the standard deviation (4 minutes).

Z = (25 - 22) / 4 = 0.75

Looking up the Z-score in a standard normal distribution table, we find that the probability of a Z-score less than or equal to 0.75 is 0.7734.

Therefore, the percentage of new machine set-ups completed within 25 minutes is approximately 77.3% (0.7734 x 100%).

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