Question 459069
Recall that the z score is based on the formula {{{z=(x-mu)/sigma}}} 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=(x-mu)/sigma}}}



{{{1.28=(x-149)/20}}} Now plug in {{{mu=149}}} and {{{sigma=20}}}



Now let's solve for x




{{{1.28=(x-149)/20}}} 



{{{1.28*20=x-149}}} 



{{{25.6=x-149}}} 



{{{25.6+149=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.