HW 3 Answer Key AEM 2100
1)
zscore = (xp)/o
Male zscore = (7569.9)/3 = 1.7
CI
j'
Female zscore = (7064.6)/2.8 = 1.93
[r/
1
The 70 inch woman is relatively taller because she has a higher zscore, which means compared to the
population of women she is taller than the 75inch man compared to the population of men.
2)
a)xbar = $33.75
standard deviation = $10
$13.75 and $53.75 are two standard deviations away from the mean. At least 75% of the prices of the
meals will be between $13.75 and $53.75.
G3
b)
For any value z, at least 1(l/z2) of the data values will lie within
z
standard deviations of the mean
Zscore for $50
(5033.75)/10 = 1.625
3
1(lI(1.625~))
= 62.1%
3
The largest proportion of meals that could be larger than $50 is (10062.1) = 37.9%
1
c)
Mean price = $33.75 x 8.0916 = 273.09 yen
Standard Deviation = $10 x 8.0916 = 80.92 yen
J!
1
This will not change your answer from part a in terms of the zscores. The only thing that will change
is now at least 75% of the prices of the meals will now be between 111.26 yen (13.75 X 8.0916) and
434.92 yen (53.75 x 8.0916). (Answers may vary).
Cj
1
b) Spain has the best environment since
it has the lowest zscore.
[
d]
3
a)
4)
a) xbar = 5309123 = 230.82 restaurants
LGl
Spain
Guatemala
Fiji
**Should add the absolute values of the
z
scores for future reference. Ok
if you didn't do
it here.
Procedures zscore
(107.9)/2.9 =
0.724
(117.9)/2.9 =
1.07
(87.9)/2.9 =
0.034
Time zscore
(4727.9)/19.6 =
0.974
(2627.9)/19.6 =
0.097
(4627.9)/19.6 =
0.923
Cost zscore
(15.114.2)/12.9 =
0.07
(47.314.2)/12.9 =
2.566
(25.314.2)/12.9 =
0.860
Combined zscore
1.768
3.733 or 3.539
1.817
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 Spring '08
 VANES,C.
 Standard Deviation, Suffolk County, Overall Cost vs, Principal Payer

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