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 $65,000. A random sample of 34 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $62,500? Assume = $6,100 The probability that the mean salary of the sample is less than $62,500 is (Round to four decimal places as needed.) Interpret the results. Choose the correct answer below. 0 A. O B. ° C. 0 D. About 84% of samples of 34 specialists will have a mean salary less than $62,500. This is not an unusual event. Only 0 84% of samples of 34 specialists will have a mean salary less than S62.500. This is an unusual event Only 84% of samples of 34 specialists will have a mean salary less than $62,500. This is an unusual event. About 0.84% of samples of 34 specialists will have a mean salary less than $62,500. This is not an unusual event.

Explanation / Answer

Mean is 65000 and s is 6100

for sample size of 34 the standard error SE is s/sqrt(N)=6100/sqrt(34)=1046.14

z is given as (x-mean)/s

P(x<62500)=P(z<(62500-65000)/1046.14)=P(z<-2.39)=1-P(z<2.39) , from normal distribution table we get 1-0.9916=0.0084 or 0.84%

answer is B

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