Question Details

Find the mean and standard deviation of the sampling distribution 



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Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.
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1.	(A) Find the mean and standard deviation of the sampling distribution of the average weekly earnings in the sample.

(B) Find probability that the mean of the sample is less than $445.

(C) Find the probability that the mean of the sample is between $445 and $455.

(D) Find the probability that the mean of the sample is greater than $460.

(E) Explain why the assumption of normality about the distribution of the average weekly earnings for employees was not involved in the answers to (A) through (D).


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A columnist for the LA Times is working to meet a deadline on a story about commuting in Los Angeles. She wants to include information about the current price of gasoline in the Los Angeles metro area, but her source person for this type of information has already gone home for the day. So she decides to take her own sample as she drives home, writing down the prices she observes as she makes her way from downtown to her neighborhood in the suburbs. Below is the data sample she obtains (units are $/gallon).

 
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	2.	(A) Do you think she has obtained a true random sample?

(B) What average price could she report, based on the above sample?

(C) What average price range could she report, based on the above sample?

(D) Do you see any issues with reporting the range calculated for (C)?





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