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?

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Answer:

145.6 seconds

Step-by-step 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:

 [tex]z=\frac{X-\mu}{\sigma}[/tex]

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:

[tex]1.28=\frac{X-120}{20}\\X=145.6\ seconds[/tex]

 Times of 145.6 seconds and over qualify for remedial training.

Q&A Education