The shape of the distribution of the time required to get an oil change at a 15-

Question

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.6 minutes, and the standard deviation is 4.6 minutes. Complete parts (a) through (c). (e) c. The sample size needs to be greater than or equal to 30. D. Any sample size could be used. (b) What is the probability that a random sample of n 45 oil changes resuits in a sample mean time less than 15 minutes? (Round to four decimal places as needed.) Suppose the manage ag ees lo pay each employee asso bonus if they meet a certain goal naty alSaturday, the oil change folity will perform 45 o changes between 10 AM and 12 PM Treat s as a random sample, there would be a 10% chance of the mean o ange time being at or below what value? This will be the goal established by the manager.

Explanation / Answer

c)here std error of mean =std deviation/(n)1/2 =0.6857

for 10 perecentile ; critical value of z=-1.2816

hence corresponding time =mean +z*Std error =15.1 minutes

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