A psychologist has developed a test called \"WETHIC” to measure the work ethic i

Question

A psychologist has developed a test called "WETHIC” to measure the work ethic in a firm's workers. The test scores approximate a Normal distribution with a mean of 74 and a standard deviation of 15. (note: this step involves manual calculation and does not require any SPSS work) For each question your answer should take the form of a complete sentence. Convert a WETHIC score of 79 into a z-score and interpret this z-score. Show your calculation. (2 pts) Convert a WETHIC score of 62 into a z-score and interpret this z-score. Show your calculation. (2 pts) 3.What proportion of workers will have a WETHIC score that is below 79? (1 pt) 4.What proportion of workers will have a WETHIC score that is below 62? (1 pt) 5. What proportion of workers will have a WETHIC score that is above 79? (1 pt) 6.What proportion of workers will have a WETHIC score that is above 62? (1 pt) 7.What proportion of workers will have a WETHIC score that is between 79 (1 pt) and 62? What are the WETHIC scores that delimit the middle 95% of the firm's workers? (2 8. pts)

Explanation / Answer

1) Z score = (79-74)/15 = 0.33 , it means score is 0.33 standard deviations above the mean

2) Z score = (62-74)/15 = -0.80 , it means score is 0.80 standard deviations below the mean

3) P(X<79)

= P(Z<0.33)

= 0.6293

d) P(X<62)

= P(Z<-0.80)

= 0.2119

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