#### Transcript Section 9.3 – Sample Means

```Section 9.3 – Sample Means
If the sample size is larger enough, then
1)
x  
The mean of a sampling
distribution of means
2)
x 

n
The standard deviation of a
sampling distribution of
means
If a sample is taken from a population that has a normal
distribution, then the sampling distribution of the means
will also be normally distributed.
Central Limit Theorem
The average age of all lawyers is 43.6 years with
a standard deviation of 5.1 years. If a law firm
employs 50 lawyers, find the probability that the
average of the group is greater than 44.2 years.
The average labor costs for car repairs for a large chain
of car repair shops is \$48.25. The standard deviation is
\$4.20. Assume the variable is normally distributed.
a. If a store is selected at random, find the
probability that the labor cost will range
between \$46. and \$48.
b. If 20 stores are selected at random, find
the probability that the mean of the
sample will be between \$46. and \$48.
```