Math 302.102 Fall 2010
Assignment #8
This assignment is due at the beginning of class on Monday, November 29, 2010.
1.
A box contains three white balls and four red balls. Suppose that 100 balls are drawn
from this box at random with replacement. Write down an exact binomial expression for the
probability that at least 50 balls drawn are red. In other words, if
X
denotes the number of
red balls drawn, determine
P
{
X
≥
50
}
. Use a suitable normal approximation to estimate this
probability. (Even if you can determine the binomial probability exactly, I still want you to do the
normal approximation.)
2.
Suppose that you play the following game. You pay $4 and roll a single standard sixsided
die. You win $
X
if an
X
appears on your roll. Thus, your net winnings (or net gain if you prefer)
is
X

4. Suppose that you then play this game 100 times. Use a suitable normal approximation
to answer the following questions.
(a)
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 Spring '08
 ISRAEL
 Math, Probability, Probability theory, $4, 1 K, $50, 1 k, 0.2%

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