Question

In: Statistics and Probability

The shape of the distribution of the time required to get an oil change at a...

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

Solutions

Expert Solution

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


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