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 130 sec and a standard deviation of 25 sec. The fastest 10% are to be given advanced training. What task times qualify individuals for such training? (Round the answer to one decimal place.)

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InesWalston InesWalston · Answer 1 · 2019-10-07T06:27:50+02:00

Answer:

The task time for the fastest 10% should be greater than 161.9 seconds.

Step-by-step explanation:

Since it is given that:

Mean = 130 seconds

Standard Deviation = 25 seconds

The fastest of the 10% can be found by finding the area corresponding to the required normal distribution curve

Thus the Z value for the normal distribution curve for the given values of mean and deviation is

Z = 1.2796

Thus the value of score can be found from the equation

[tex]Z=\frac{X-\overline{X}}{\sigma }[/tex]

Applying values we get

[tex]1.2796=\frac{X-130}{25}\\\\\therefore X=161.99[/tex]