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 $50,500. A random sample of 44 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $58,000? Assume = $6,500. The probability that the mean salary of the sample is less than $58,000 is Round to four decimal places as needed.) Interpret the results. Choose the correct answer below. A. O B. ° C. 0 D. Only 0.54% of samples of 44 specialists will have a mean salary less than $58,000. This is an unusual event. About 0.54% of samples of 44 specialists will have a mean salary less than $58,000. This is not an unusual event. Only 54% of samples of 44 specialists will have a mean salary less than $58,000. This is an unusual event. About 54% of samples of 44 specialists will have a mean salary less than $58,000. This is not an unusual event.

Explanation / Answer

In step 1, we will divide standard deviation by sqrt of 44 which is 6.63 so we will get 6500/6.63= 980.392

Since =60500 and =980.32 we have:

P ( X<58000 )=P ( X<5800060500 )=P (X)/<(5800060500)/980.32)

Since x/=Z and (5800060500)/980.32=2.55 we have:

P (X<58000)=P (Z<2.55)

Step 3: Use the standard normal table to conclude that:

P (Z<2.55)=0.0054 which is only 0.54% of samples of 44 specialists will have mean salary less than $58000. This is an unusual event.

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