Statistics and Probablity

Question

The college Physical Education Department offered an Advanced First Aid course last summer. The scores on the comprehensive final exam were normally distributed, and the Z scores for some of the students are shown below. 

(When typing in the names, try to put them in the order they appear in the list, and please do not use commas.)

Robert, -0.69      Juan, 1.32          Susan, 2.01

Joel, -1.73                 Jan, 1.15            Linda, 0.00

Answer the following questions based on this information.

Q4a. Which students scored above the mean? 

Q4b. Which student scored at the mean? 

Q4c. Which students scored below the mean  

Q4d. If the mean score was 157 with a standard deviation of 19, what was the final score for Robert? Please round your answer to a whole number. 

Q4e. Using the mean of 157 and the SD of 19, what was the mean score for Susan? Please round your answer to a whole number. 

Q4f. Using the mean of 157 and the SD of 19, what was the mean score for Linda? Please round your answer to a whole number

Answer 1

a-c.

Remember that whenever you see a z-score, you want to think of the standard normal (mean = 0 and variance = 1). So, you can look at z-tables to determine if positive or negative values of z correspond to above or below the mean. Also note that z = 0 is a special case that is exactly at the mean of 0.

d-f.

The z-score is equal to the following:

z-score = (X - mean)/(standard deviation)

where X is in this case, the score for a particular person. You can use this equation to solve for the scores.