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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 16.2 minutes, and the standard deviation is 3.4 minutes.
(a) What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?
Round to 4 decimal.
(b) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain gol. On a typical Sunday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, what mean oil-change time would there be a 10% chance of being at or below? 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.
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In addition, record the values for the UCL, center line, and LCL. Also, record any points that are out of control. Use a z-value of three.
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