Find the probability and interpret the results. If convenient, use technology to

Question

Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $66,000. A random sample of 30 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $62,000? Assume = $6,500. The probability that the mean salary of the sample is less than $62,000 is (Round to four decimal places as needed.) Interpret the results. Choose the correct answer below. A. B. C. 0 D. About 0.04% of samples of 30 specialists will have a mean salary less than $62,000. This is not an unusual event. About 4% of samples of 30 specialists will have a mean salary less than $62,000. This is not an unusual event. Only 0.04% of samples of 30 specialists will have a mean salary less than $62,000. This is an extremely unusual event. Only 4% of samples of 30 specialists will have a mean salary less than $62,000. This is an extremely unusual event.

Explanation / Answer

pop. mean = 66000
N = 30
Sigma = 6500

P(Xbar<62000)
= P(Z< 62000-Mean / (Sigma/sqrt(n)) )
= P(Z< (62000-66000)/(6500/sqrt(30)) = P(Z<-3.3706)  
= .000375
=~.0004

Only .04% of samples of 30 specs. will have mean salary less than 62000. This is an extremely unusual event.

C is correct

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