Answer the following question using information learned in chapter 5 z-Scores and
location in a distribution. Please show your work. Not showing your work will only earn
you partial credit of 5 points.
1. A set of mathematics exam scores has a mean of 70 and a standard deviation of 8.
A set of English exam scores has a mean of 74 and a standard deviation of 16. For
which exam would a score of 78 have a higher standing?
z(math) = (X - μ) / σ
= (78 - 70) / 8
= 8 / 8
= 1
z(english) = (X - μ) / σ
= (78 - 74) / 16
= 4 / 16
= 0.25
Mathematics has a higher standing
2. In a population of scores a raw score with the value of 83 corresponds to a Z of
+1.00 and a raw score of 86 corresponds to a Z of +2.00. What is the mean and
standard deviation of this population?
1.00=
83−µ
σ
σ= 83-μ
2.00=
86−µ
σ
2.00=
86−µ
83−µ
2(83-
μ)=86-μ
166-2μ=86-μ
-μ=-80
