Question

1. The time necessary to complete a certain assembly-line task varies according to many factors: fatigue or freshness, worker skill, whether the required parts are available promptly, and so forth. Suppose that this variation may be adequately modeled using a normal distribution with mean 15 minutes and standard deviation 2 minutes.  The quickest 5% of the assembly times are to be rewarded. How fast must an assembly be performed in order to be rewarded?  

   		11.71 minutes
   		1.50 minutes
   		10.34 minutes
   		12.92 minutes
   		12.44 minutes

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 15

S.d = 2

From z table, P(z>1.645) = 5%

1.645 = (x - 15)/2

X = 18.29