Question

The time 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 of 120 seconds and a standard deviation of 20 seconds.  The fastest 10% are to be given advanced training. What task time qualifies individuals for such training? (Remember the fastest times takes the least amount of time.) Use Excel to find your answer .Round your answer to the nearest second.  

Answer 1

Given that the time is taken to perform a certain task follows a normal distribution with a mean of = 120 seconds and a standard deviation of = 20 seconds.

and given that the fastest 10% is to be given advanced training.

So, to find the limit of the top 10% of the normal distribution we need to find the Z score for the probability value of 0.90 because the total probability of the distribution is 1.00 and the Z table or the excel formula uses probability values from the left.

The Z score is calculated using excel formula for normal distribution which is =NORM.S.INV(0.9) thus result in Z =1.282.

Now using the Z formula the task time is calculated as:

Rounding to the nearest second it is X = 146 seconds.

So, the task time of 146 seconds qualifies individuals for such training.