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CLT(Central Limit Theorem)
and Normal Probabilities  Draw a normal graph for each
problem. Include x scores and z scores and shade appropriate areas.
1.
Replacement times for CD players are normally distributed with a mean of 7.1 years and
a standard deviation of 1.4 years. A) Find the probability that a randomly selected CD
player will have a replacement time
less than 8.0 years
. B) If 45 CD players are
randomly selected, how many of them would you expect to have a replacement time less
than 8.0 years. C) Find the probability that 45 randomly selected CD players will have a
mean replacement time
greater than 7.0 years
.
2.
Assume that the weights of paper discarded by households each week are normally
distributed with a mean of 9.4 lb and a standard deviation of 4.2 lb. A) Find the
probability of randomly selecting a household and getting one that discards
between 5.0
lb and 8.0 lb
of paper in a week. B) If 16 households are randomly selected, find the
probability that the mean amount of paper they discard in a week is
more than 10.0 lb
.
3.
One classic use of the normal distribution is inspired by a letter to Dear Abby in which a
wife claimed to have given birth 308 days after a brief visit from her husband, who was
serving in the Navy. The lengths of pregnancies are normally distributed with a mean of
268 days and a standard deviation of 15 days. A) Given this information, find the
probability of a pregnancy lasting
308 days or longer
. B) If 25 randomly selected
women are put on a special diet just before they become pregnant, find the probability
that their lengths of pregnancy have a mean that is
less than 260 days
(assuming that the
diet has no affect  which means that the original data still applies).
4.
Men spend an average of 11.4 min in the shower. Assume that the times are normally
distributed with a standard deviation of 1.8 min. A) If 33 men are randomly selected, how
many of them would you expect to spend
at least 10.0 min
in the shower? B) If 33 men
are randomly selected, find the probability that their shower times have a mean
between
11.0 and 12.0 minutes.
5.
According to the International Mass Retail Association, girls aged 13 to 17 spend an
average of $31.20 on shopping trips in a month. Assume that the amounts are normally
distributed with standard deviation of $8.27. A)What percentage of girls in that age
category
spend
between $34.00 and $40.00
in one month? B) If 85 girls in that age
category are randomly selected, what is the probability that their mean monthly shopping
expense is
between $30.00 and $33.00?
6.
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
Mensa is an organization for people with high IQs, and eligibility requires an IQ
above
131.5
. A) What
percentage
of people meet the Mensa requirement? B) In a typical
region of 75,000 people, how many are eligible for Mensa? C) If 25 people are randomly
selected, what is the probability that the mean of their IQ's is
above 105
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 Spring '11
 Hughes
 Statistics, Central Limit Theorem, ZScores

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