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.
-97.5% of the time, the bolt is inserted in less than which time value? Round to the nearest whole number.
A)23 minutes
B)19 minutes
C)7 minutes
D)15 minutes

Question

Quizplus · Accepted Answer

The 97.5th percentile in a normal distribution corresponds to a Z-score of approximately 1.96. Using the formula for converting Z-scores to raw scores (X = μ + Zσ), where μ is the mean and σ is the standard deviation, we get X = 15 + (1.96)(4) = 22.84, which rounds to 23 minutes.

Use the Following Information for Following Questions