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Chapter 7: Problem 81

The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 120 seconds and a standard deviation of 20 seconds. The fastest \(10 \%\) are to be given advanced training. What task times qualify individuals for such training?

Short Answer

Expert verified
Individuals who can complete the task in 125.6 seconds or less qualify for advanced training.

Step by step solution

01

Identifying known values

From the problem, ge can identify that the mean (\(\mu\)) of the distribution is 120 seconds and the standard deviation (\(\sigma\)) is 20 seconds. Furthermore, we need to find the cut-off time for the fastest 10%, or the 90th percentile (since these are the top performers), which in Z-score is approximately 1.28.
02

Finding the cut-off time

Using the Z-score formula, which is Z = (X - \(\mu\)) / \(\sigma\), we solve for X, the cut-off time: X = Z* \(\sigma\) + \(\mu\). Substituting the known values, we find X = 1.28 * 20 + 120 = 125.6 seconds.
03

Conclusion

Therefore a person will qualify for advanced training if they can perform the job task in less than or equal to 125.6 seconds.

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Most popular questions from this chapter

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