STAT 420
Spring 2014
Homework 1:
Due February 4 by 7:00pm
Exercise 1
(a) At Anytown College, the heights of female students are normally distributed with
mean 66 inches and standard deviation 1.5 inches. The heights of male students are
also normally distributed with mean 69 inches and standard deviation 2 inches. For
Homecoming, a male student and a female student are selected independently at ran
dom to be the King and the Queen. What is the probability that the female student
selected to be the Queen is taller than the male student selected to be the King?
(b) Suppose that a population of married couples in Anytown have heights in inches,
X
for the wife, and
Y
for the husband. Suppose that
(
X,Y
)
has a bivariate normal
distribution with parameters
μ
X
= 66
,
σ
X
= 1
.
5
,
μ
Y
= 69
,
σ
Y
= 2
,
ρ
= 0
.
44
. What is
the probability that the wife is taller than her husband?
Exercise 2
Every month, the government of Neverland spends
X
million dollars purchasing guns and
Y
million dollars purchasing butter. Assume
X
and
Y
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 Spring '08
 Stepanov
 Statistics, Normal Distribution, Standard Deviation, σx, µx, Burger Queen, oreo cookies

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