Question

The shape of the distribution of the time required to get an oil change at a 20?-minute

?oil-change facility is unknown.? However, records indicate that the mean time is 21.1 minutes?, and the standard deviation is 4.2 minutes.

Suppose the manager agrees to pay each employee a? $50 bonus if they meet a certain goal. On a typical? Saturday, the? oil-change facility will perform 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random? sample, there would be a? 10% chance of the mean? oil-change time being at or below what? value? This will be the goal established by the manager.

There is a? 10% chance of being at or below a mean? oil-change time of ____ minutes

Answer 1

In question given , On a typical? Saturday, the? oil-change facility will perform 35 oil changes between 10 A.M. and 12 P.M.

that is here sample size = n = 35 .

If the sample size is greater than 30 then we use normal distribution .

In question given , mean =    and standerd deviation =

And here they ask to find , mean value at which a ? 10% chance of being at or below a mean? oil-change time.

That is in normal distribution curve they given below 10% area .

   

Find z-score at area =0.10, use excel command as =NORMSINV(0.10) then hit enter you will get z-score = -1.28.

There they ask find sample mean , that is .

Z-score formula for sample mean is as,

              we know all values ,putting these value we find value of xbar .

            

           

             

             

            

There is a? 10% chance of being at or below a mean? oil-change time of 20.2 minutes