Answers to Homework 5
Pg. 160162: 23, 24, 26 & 28
Pg. 195197: 2, 5(a,d), 6(b, c), 7(a,c), 8(b,d), 10(a,c),
11(b, c, d), 12a, 14(a, b, c), 15a, 16a, 18a, 19(a,b) & 21(a, b, c)
23.
a)
Z =
X
–
μ
4340
= 3/2 = 1.5
OR
b) 6050
= 10/20 = 0.5
σ
2
20
I would expect a better grade on the exam with a 43 because when the score is standardized a
score of 1.5 is higher than a score of .50. I would rather be one and half standard deviations
above the mean than only a half of a standard deviation.
24.
a)
Z =
X
–
μ
5560
= 5/5 = 1
OR
b) 4050
= 10/20 = 0.5
σ
5
20
I would expect a better grade on the exam with a 40 because I would rather be a half standard
deviation below the mean than a full standard deviation below the mean.
26.
a)
Z =
X
–
μ
4838
= 10/20 =
0.5
σ
20
(Z*
σ
) +
µ
=
X
(0.5*10) + 50 = 5 +50 =
55
b)
Z =
X
–
μ
4038
= 2/20 =
0.1
σ
20
(Z*
σ
) + µ
=
X
(0.1*10) + 50 = 1 +50 =
51
c)
Z =
X
–
μ
3038
= 8/20 =
0.4
σ
20
(Z*
σ
) + µ
=
X
(0.4*10) + 50 = 4 +50 =
46
d)
Z =
X
–
μ
1838
= 20/20 =
1
σ
20
(Z*
σ
) + µ
=
X
(1*10) + 50 = 10 + 50 =
40
28.
a)
µ
= 0+6+4+3+12/5 = 25/5 =
5
X
XM
(XM)
2
0
5
25
6
1
1
4
1
1
3
2
4
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12
7
49
0
80
SS / (N) = variance
√variance = SD
80/(5) = 16
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 Fall '09
 DianeAlonso
 Standard Deviation, σ B, zscore probability, Z=X–μ

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