Sampling Distributions-Population Mean Central Limit Theorem If a random sample

Question

Sampling Distributions-Population Mean Central Limit Theorem If a random sample of size n is drawn from a population X with mean x and variance , then the sample mean, X , has approximately a Normal distribution with mean and variance -n Note: The approximation improves as the sample size increases Alternative CLT definition: IfXi, X2, ,x, cormprise a random sample of n observations taken from a population X with mean , and variance ox, and if X is the sample mean, then as n the limiting form of the distribution of: 1 is the Standard Normal Distribution. Repair time (X) for an oil change at a car dealership has a population mean .-50 minutes and a population standard deviation ,-7 minutes. If a random sample of 100 oil changes is selected, what is the probability that the sample mean is below 48.5 minutes?

Explanation / Answer

mean is 50 and s is 7. here N=100 thus, standard error is s/sqrt(N)= 7/sqrt(100)=0.7

P(x<48.5)=P(z<(48.5-50)/0.7)=P(z<-2.14) or 1-P(z<2.14)

from normal distribution table we get 1-0.9838 =0.0162 or 1.62%

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