SOLUTION: Please Help!! Thank you!!! The college Physical Education Department offered an Advanced First Aid course last summer. The scores on the comprehensive final exam were normally dis

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Question 459069: Please Help!! Thank you!!!
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.
Robert, 1.28 Juan, 1.89 Susan, –1.95
Joel, 0.00 Jan, –0.96 Linda, 1.46
If the mean score was μ = 149 with standard deviation σ = 20, what was the final exam score for each student? (Round your answers to the nearest whole number.)
Robert
Joel
Jan
Juan
Susan
Linda
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that the z score is based on the formula z=%28x-mu%29%2Fsigma where mu is the mean and sigma is the standard deviation. (note: the z score tells you where this score lies with respect to the mean and how far it is away from the mean)


In this case, you're given the value of z (the standard z score) for each person, and they want you to find x (the actual score)


So in the case of Robert for instance, he has a z score of 1.28


So z=1.28 for Robert.


Plug this into the formula above to get


1.28=%28x-mu%29%2Fsigma


1.28=%28x-149%29%2F20 Now plug in mu=149 and sigma=20


Now let's solve for x



1.28=%28x-149%29%2F20


1.28%2A20=x-149


25.6=x-149


25.6%2B149=x


174.6=x


x=174.6


So in Robert's case, when x=174.6, then z=1.28


So Robert's actual score is 174.6


Round this to the nearest whole number (as instructed) to get 175.


So Robert's final exam score to the nearest whole number is 175.


Simply repeat these steps to find the final exam scores for the rest of the students.