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 145 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.)

Answer 1

Answer:

A task time of 177.125s qualify individuals for such training.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

A distribution that can be approximated by a normal distribution with a mean value of 145 sec and a standard deviation of 25 sec, so $\mu = 145, \sigma = 25$.

The fastest 10% are to be given advanced training. What task times qualify individuals for such training?

This is the value of X when Z has a pvalue of 0.90.

Z has a pvalue of 0.90 when it is between 1.28 and 1.29. So we want to find X when $Z = 1.285$.

So

$Z = \frac{X - \mu}{\sigma}$

$1.285 = \frac{X - 145}{25}$

$X - 145 = 32.125$

$X = 177.125$

A task time of 177.125s qualify individuals for such training.