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 ​$63,000. A random sample of 32 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than ​$59 comma 500​? Assume o=​$6,300. The probability that the mean salary of the sample is less than ​$59,500 is nothing. ​(Round to four decimal places as​ needed.) Interpret the results.

Choose the correct answer below

. A. About 8​% of samples of 32 specialists will have a mean salary less than ​$59,500. This is not an unusual event.

B. Only 8​% of samples of 32 specialists will have a mean salary less than ​$59,500. This is an extremely unusual event.

C. About 0.08​% of samples of 32 specialists will have a mean salary less than ​$59,500. This is not an unusual event.

D. Only 0.08​% of samples of 32 specialists will have a mean salary less than ​$59,500. This is an extremely unusual event.

Answer 1

mena = 63000 , sigma =6300 , n = 32

P(x<59500)
= P(z < (x - mean)/(sigma/sqrt(n))
= P(z< (59500 - 63000)/(6300/sqrt(32))
= P(z < -3.1427)
= 0.0008

D. Only 0.08​% of samples of 32 specialists will have a mean salary less than ​$59,500. This is an extremely unusual event.