Question

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 10% of the assembly times are to be rewarded. How fast must an assembly be performed in order to be rewarded?  

Answer 1

Solution:

Given: The time necessary to complete a certain assembly-line task varies according to a normal distribution with mean 15 minutes and standard deviation 2 minutes.  

The quickest 10% of the assembly times are to be rewarded.

That is the assembly times which are in bottom 10% of the distribution are to be rewarded.

We have to find assembly time to be performed in order to be rewarded.

That is find x value such that:

P( X < x ) = 10%

P( X < x ) = 0.10

Thus find z value such that:

P( Z< z ) = 0.10

Look in z  table for Area = 0.1000 or its closest area and find corresponding z value.

Area 0.1003 is closest to 0.1000 and it corresponds to -1.2 and 0.08

Thus z = -1.28

Now use following formula to find x value:

minutes.

Thus an assembly time to be performed in order to be rewarded is 12.44 minutes.