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 150 sec and a standard deviation of 15 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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ChiKesselman ChiKesselman · Answer 1 · 2020-03-17T04:15:01+01:00

Answer:

If the task is performed in less than or equal to 130.8 seconds, then, the individuals qualify for advanced training.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 150 sec

Standard Deviation, σ = 15 sec

We are given that the distribution of time taken is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.10

P(X < x)

[tex]P( X < x) = P( z < \displaystyle\frac{x - 150}{15})=0.10[/tex]

Calculation the value from standard normal z table, we have,

[tex]\displaystyle\frac{x - 150}{15} = -1.282\\x = 130.8[/tex]

Thus, if the task is performed in less than or equal to 130.8 seconds, then, the individuals qualify for advanced training.