Statistics for Decision-Making Submit Time Remaining: 01:27:27 Quiz: Week 7 Quiz

Question

Statistics for Decision-Making Submit Time Remaining: 01:27:27 Quiz: Week 7 Quiz 12 of 19 (2 complete) This Quiz: 60 pts po This Question: 4 pts 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 $60,000. A random sample of 45 specialists is drawn from this population What is the probability that the mean salary of the sample is less than $57,500 Assume S5900 The probability that the mean salary of the sample is less than $57,500 is Round to four decimal places as needed) Interpret the results. Choose the correct answer below A. Only 0.22% of samples of 45 specialists will have a mean salary less than S57,500 This is an unusual event O B. About 22% of samples of 45 specialists will have a mean salary less than S5 7,500 This is not an unusual event O c. Only 22% of samples of 45 specialsts will have a mean salary less than S5 7,500 This is an unusual event 0 D. About 022% of samples of 45 specialists will have a mean salary less than SS7,500 This is not an unusual event Click to select your answer(s) Type here to search a wa

Explanation / Answer

Solution:

The probability that the mean salary of the sample is less than$57,500 is obtained below:

Let X be the random variable defined by the salary for environmental compliance specialists follows normal distribution with mean () $60,000, standard deviation () $5,900, and sample size (n) 45.

The required probability is,
P(x < 57500) = P[x - 60000/(5900/45) 57500- 60000/(5900/45)]
= P[z -2.84]
= 0.0022
The probability that the mean salary of the sample is less than $57,500 is 0.0023.

The probability value for the mean salary of the sample is less than $57,500 is 0.0022 (or 0.22%) which is less than the 0.05 (or 5%). This indicates that the probability value is very small. Thus, the probability value for the mean salary of the sample is less than $57,500 is extremely unusual event.
A) Only 0.22% of samples of 45 specialists will have a mean salary less than $57,500. This is an unusual event.

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