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

Answer:

The task times is  $x =90.77 \ s$

Step-by-step 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

      $P(X  <  x) =  0.10$

=>    $P(X  <  x) = P( \frac{X - \mu}{\sigma }  <  \frac{x - 110}{15} )  = 0.10$

Generally $\frac{X - \mu}{\sigma }   = Z (The  \ standardized \  value  \  of  X )$

=>   $P(X  <  x) = P( Z <  \frac{x - 110}{15} )  = 0.10$

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

      $z -score =  -1.282$  

So

      $\frac{x - 110}{15}   =  -1.282$

=>    $x =90.77 \ s$