8. Suppose you got a catfish that was bigger than 90% of the others. How much did your
catfish weigh?
a. 90% * 3.6 = 3.24 pounds
b. 3.6 + .90(.8) = 4.32 pounds
c. 3.6 + 1.28(.8) = 4.62 pounds
d. 3.6 + .90(3.6) = 6.84 pounds
Suppose X has a normal distribution with mean 10 and variance 4, Y has a normal
distribution with mean 20 and variance 9, and X and Y are independent.
9. The mean of
X+Y is 30.
10. You cannot find the variance of X+Y with only the above information.
11. What is the variance of 2X?
12. You want to estimate the average starting salary for recent business majors and you
want the margin of error of your results to be no more than $500. You are planning to
take a random sample of recent business major graduates and ask them for their starting
salaries. Assume that the standard deviation of starting salaries for all recent business
major graduates is $8000 and that you want to have 95% confidence in your results.
a. What should your sample size be?
n =
= 983.45 = 984 people
b. Would the margin of error increase or decrease if the sample size was 1,000?
(Assume nothing else changes in the problem.)
The MOE would decrease because the results are more precise with a larger
sample size.
3
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 Fall '11
 Johnson
 Statistics, Normal Distribution, Standard Deviation, ZScores, math exam

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