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Practice Problems for Central Limit Theorem
© 2010 Radha Bose FSU Department of Statistics
1
1.
Let us suppose that the weights of baby elephants are Normally distributed with mean 224 lbs and
standard deviation 53 lbs.
(a) What is the probability that the mean weight of 18 randomly selected baby elephants is more than
245 lbs?
(b) What is the probability that a single randomly selected baby elephant weighs more than 245 lbs?
(c) Is it more likely that the weight of a single baby elephant or the mean weight of 18 baby elephants will
be more than 245 lbs?
(d) Your answer to part (c) illustrates that
(A) means are less consistent (tend to stray from their center more) than individual observations.
(B) means are more consistent (stay closer to their center more) than individual observations.
(e) If there is a 0.11 probability that the mean weight of 18 baby elephants is above a certain amount but
less than 224 lbs, what is that amount?
2.
A certain psychological test that determines if a person has more of a "male brain" or a "female brain"
is designed so that the mean score for men is 50.
We may assume that the standard deviation of men's
scores on this test is 25.
(a) Is it safe for us to assume that the distribution of
X
= the mean score of a SRS of 12 men who take
the test
Normal enough for us to use Normal probability calculations?
State YES or NO and give a reason
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 Fall '11
 RADHABOSE
 Central Limit Theorem, Probability, Standard Deviation

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