Central Limit Theorem

1
Central Limit Theorem If the data comes from a
distribution with a mean m and a variance s2,
then the sampling distribution of the average
will be approximately normally distributed with a
mean m and variance s2/n regardless of the
underlying distribution of the data. The
approximation gets better as n increases.
2
A good question for exam 2 Q Why is the
sampling distribution approximately normally
distributed regardless of the underlying
distribution of the data? A Central Limit
Theorem
3
A single fair 6-sided die
m 3.5, s2 2.9167
4
Average of 2 fair 6-sided dice
m 3.5, s2 2.9167 / 2
5
Average of 3 fair 6-sided dice
m 3.5, s2 2.9167 / 3
6
The mean weight of chocolate chip cookies is 0.75
ounces and the standard deviation is 0.1 ounce.
What is the probability that 10 cookies weigh
more than 8 ounces?
X1 weight of cookie 1 X10 weight of cookie
10
7
Individual McDonalds french fries have a mean of
12 calories with a standard deviation of 2
calories. There are 50 french fries in a large
container of fries. A calorimeter attempts to
measure the total number of calories for the
container of fries, but is only able to measure
up to a maximum of 620 calories. Given that the
calorimeter is maxed out, what is the
probability that the total number of calories is
less than 635?
8
The mean song length of songs played at a radio
station is 2.3 minutes with a standard deviation
of 0.3 minutes. 90 of the time it takes between
21.5 minutes and _________ minutes to listen to
10 songs. The time to process payment
information at an office supplies web site has a
mean of 63 seconds and a standard deviation of 9
seconds. What is the probability that it will
take longer than 40 minutes for 36 customers to
process payment information?