Use the following information for following questions . The mean time it takes for workers at a factory to insert a
delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the
distribution of time is approximately normally distributed.
-For a randomly selected worker, what's the approximate probability the bolt will be inserted in 19 minutes or less? Round to the nearest whole percent.
A)50%
B)84%
C)18%
D)16%

Question

Quizplus · Accepted Answer

To find the probability, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (19 minutes), μ is the mean (15 minutes), and σ is the standard deviation (4 minutes). Plugging in the values, we get Z = (19 - 15) / 4 = 1. A Z-score of 1 corresponds to the 84th percentile in a standard normal distribution, meaning there's an approximately 84% chance the bolt will be inserted in 19 minutes or less.

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