This preview shows pages 1–5. Sign up to view the full content.
Distribution of the Sample Mean
●
Learning objectives
Understand the concept of a sampling distribution
Describe the distribution of the sample mean for
samples obtained from normal populations
Describe the distribution of the sample mean for
samples obtained from a population that is not
normal
1
2
3
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Distribution of the Sample Mean
●
This is great if our random variable
X
has a
normal distribution
●
However … what if
X
does not
have a normal
distribution
●
What can we do?
Wouldn’t it be very nice if the sampling distribution for
X
also was normal?
This is almost true …
Distribution of the Sample Mean
●
The
Central
Limit
Theorem
states:
Regardless of the shape of the distribution,
the sampling distribution becomes approximately
normal as the sample size n increases
●
Thus
If the random variable
X
is normally distributed, then
the sampling distribution is normally distributed for any
sample size
For all other random variables
X
, the sampling
distributions are approximately normally distributed if
n
is 30 or higher
Helpful Hint:
Study Example 5 on pp.426427 of your textbook.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Distribution of the Sample Mean
Example
The most famous geyser in the world, Old Faithful in Yellowstone
Nat’l Park, has a mean time between eruptions of 85 minutes and
a standard deviation of 21.25 minutes.
The distribution of time
interval between eruptions is not normal.
1.
What is the probability that a randomly selected time interval will
be less than 75 minutes?
2.
What is the probability that a random sample of 20 time intervals
will have a mean less than 75 minutes?
3.
What is the probability that a random sample of 30 time intervals
will have a mean less than 75 minutes?
4.
What is the probability that a random sample of 30 time intervals
will have a mean longer than 100 minutes?
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 08/04/2008 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.
 Spring '08
 sims

Click to edit the document details