Let x be the random variable representing the amount of sleep each adult in New

Question

Let x be the random variable representing the amount of sleep each adult in New York city got last night. Consider a sampling distribution of sample means, x-bar. a) As the sample size becomes large, what distribution does the x-bar distribution approach? The shape of the distribution of the time required to get an oil change at a ten minute oil-change facility is unknown. However, records indicate that the mean time for an oil change is 11.4 minutes, and the standard deviation for oil-change time is 3.2 minutes. a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? b) What is the probability that a random sample of n = 40 oil changes results in a sample mean time of less than 10 minutes. Write your answer in correct probability notation. c) Sketch the normal curve and label the measurements.

Explanation / Answer

(2) (a) As the sample size becomes larger, X bar follows a Normal distribution.   

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