Download Population (5, 10, 15, 20, 25)…all samples of size 2 – mean

Sampling Distribution
of a sample Means
Section 7.3
Let’s finish the class height….
Population (5, 10, 15, 20, 25)…all samples of
size 2 – mean.
What should a sampling
distribution for rolling 1 dice 20
times look like?
What should a sampling distribution
for the mean when rolling 2 dice 20
times look like?
What should a sampling distribution
for the mean when rolling 10 dice
20 times look like?
Simulation of Central Limit
Theorem

http://onlinestatbook.com/simulations/CLT/
clt.html
*Averages are less variable than individual observations!
Central Limit Theorem
When n is sufficiently large, the sampling
distribution of x is well approximated by a
normal curve, even if the population
distribution is not itself normal. (if n>30)
To clarify:

A sample mean ( X ) based on a large n
will tend to be closer to the population
mean (  X) than one based on a small n.

The larger the sample size, n, the smaller
the standard deviation.
Properties of a Sampling
Distribution of Sample Means
   
x


x 

n
Shape is approximately normal since
 Population is normal, or
 Central Limit Theorem (n
 30)
If a population has a mean equal to 52 and a
standard deviation equal to 3.4 and n = 100

What is the mean of the sample mean?

What is the standard deviation of the sample
mean?

Describe the shape of the sampling distribution.
Thus…..
value  mean
z
st.dev
x  x
z
x
z
x

n
The amount of spaghetti sauce that fills a glass jar is
normally distributed with   850 g . and   8 g . Find the
probability that

A jar, selected at random, is between 848 g. and 855 g.

A sample of 24 jars has a mean weight between 848 and
855 grams.
The heights of kindergarteners are approximately normal
with   39in and   2in . A class of 30 is used as a
sample. What is the probability that the sample mean is
between 38 and 40?
What would be different if I only asked the probability of
finding a randomly selected kindergartner who is between
38 and 40 inches?
The mean of song duration is   13.8sec and   11.8sec
. If the population is normally distributed, find the probability
that in a sample of 30 songs, the duration is more than 14.5
seconds?
A soft drink as an average of 12 oz. Suppose x is normally
distributed with standard deviation of 0.16 oz. If 16 cans
are randomly selected and the volume is checked, what’s
the probability that the average of the sample is more than
12.5 oz?
The composite scores of individual students on the ACT
college entrance examination in 2009 followed a Normal
distribution with mean 21.1 and standard deviation 5.1.

What is the probability that a randomly chosen student scored 23 or
higher?

What is the probability that a SRS of 50 students had a mean score
of 23 or higher?
Homework

Worksheet on SD of Means