Question

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.)

Answer 1

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

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:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

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

P(X < x)

`P( X < x) = P( z < \displaystyle(x - 150)/(15))=0.10`

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

`\displaystyle(x - 150)/(15) = -1.282\\x = 130.8`

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