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Quantitative Research Methods
Jamie Boyer
Week 2
Chapter 6
36.
An investment will be worth $1000, $2000, or $5000 at the end of the year.
The
probabilities of these values are .25, .60, and .15, respectively.
Determine the mean and variance
of the worth of the investment.
Let X be the investment worth. The mean is:
E(X) = 1000 * 0.25 + 2000 * 0.60 + 5000 * 0.15 = 2200
the variance is:
Var(X) = 1000^2 * 0.25 + 2000^2 * 0.60 + 5000^2 * 0.15  2200^2
Var(X) = 1560000
39.
A Tamiami shearing machine is producing 10% defective pieces, which is abnormally high.
The quality control engineer has been checking the output by almost continuous sampling since
the abnormal condition began.
What is the probability that in a sample of 10 pieces:
a.
Exactly 5 will be defective?
10.
choose 5 * 0.1^5 * 0.9^5 = 252 * 0.1^5 * 0.9^5
= 0.0014880348
b.
5 or more will be defective?
10 choose 5 * 0.1^5 * 0.9^5 + 10 choose 6 * 0.1^6 * 0.9^4 + 10 choose 7 * 0.1^7 *
0.9^3 + 10 choose 8 * 0.1^8 * 0.9^2 + 10 choose 9 * 0.1^9 * 0.9^1 + 10 choose 10 *
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 Spring '10
 BARCUS

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