Question

The time that it takes a randomly selected employee to perform a certain task is approximately normally distributed with a mean value of 120 seconds and a standard deviation of 20 seconds. The slowest 10% (that is, the 10% with the longest times) are to be given remedial training. What times (the lowest value) qualify for the remedial training?

Answer 1

145.6 seconds

Explanation:

Mean time (μ) = 120 seconds

Standard deviation (σ) = 20 seconds

In a normal distribution, the z-score for any time, X, is given by:

`z=(X-\mu)/(\sigma)`

The slowest 10% correspond to the 90th percentile of a normal distribution, which has a corresponding z-score of roughly 1.28. The lowest time that requires remedial training is:

`1.28=(X-120)/(20)\\X=145.6\ seconds`

Times of 145.6 seconds and over qualify for remedial training.