The shape of the distribution of the time required to get an oil change at a 10

Question

The shape of the distribution of the time required to get an oil change at a 10 minuteoil change facility is unknown. However, records indicate that the mean time is 11.2 minutes, and standard deviation is 4.6 minutes.

Suppose a 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.

Explanation / Answer

mean = 11.2 ,sd = 4.6 , , n = 35

Z = (X - 11.2)/(4.6/sqrt(35))

P( X < X*) = 0.1

P(Z< (X* - 11.2)/(4.6/sqrt(35)) = 0.1

(X* - 11.2)/(4.6/sqrt(35)) = - 1.282

X* = 11.2 - 1.282 *(4.6/sqrt(35)) =10.203

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