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 110 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.) seconds or less

Answer 1

The task times is
`x =90.77 \ s`

Explanation:

From the question we are told that

The mean is
`\mu  =  110 \ sec`

The standard deviation is
`\sigma =  15 \  sec`

Generally the task times that qualify individuals for such training is mathematically represented as

`P(X  <  x) =  0.10`

=>
`P(X  <  x) = P( (X - \mu)/(\sigma )  <  (x - 110)/(15) )  = 0.10`

Generally
`(X - \mu)/(\sigma )   = Z (The  \ standardized \  value  \  of  X )`

=>
`P(X  <  x) = P( Z <  (x - 110)/(15) )  = 0.10`

Generally the z -score of 0.10 from the z-table is

`z -score =  -1.282`

So

`(x - 110)/(15)   =  -1.282`

=>
`x =90.77 \ s`