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 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.)

________ seconds or less

Answer 1

214.5 seconds or less time will qualify individuals for such training

Explanation:

given that 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 25 sec.

i.e. X the time that it takes a randomly selected job applicant to perform a certain task is N(150,25)

The fastest 10% are the ones who are above the 90th percentile

We know 90th percentile for Z std normal score is 1.28

Corresponding X score would be

`x=\mu+1.28 \sigma\\X= 150+1.28(25)\\= 214.50`

Round off to one decimal

214.5 seconds or less time will qualify individuals for such training