#### Transcript of 5.1 Sampling Distribution of a Sample Mean

Mean: average of all data collected

(x1 +x2 + x3) / N

Sample mean is the average of observations in a normally distributed sample

**5.1 Sampling Distribution of a Sample Mean**

Formulas for sample means

N= 36

u= 240

S = 18

So sample mean is 240 as well. Sample standard deviation is 18/sqrt36 or 18/6 or 3

Example 1

You take an SRS of size 36 from a population with mean 240 and standard deviation 18. Find the mean and standard deviation of the sampling distribution of your sample mean.

s= 184.81

n= 20

184.81/sqrt20 or 184.81/4.47 or 41.345

Example 2

The standard deviation of the population of service call lengths s= 184.81 seconds. The length of a single call will often be far from the population mean. If we choose an SRS of 20 calls, the standard deviation of their mean length is

That's where the

Central Limit Theorem

comes in....

What about when the sample distribution is not normal?

*N is considered large if n> 30

According to the Central Limit Theorem when n is large* then the distribution is approximately Normal.

The solid line shows the actual distribution whereas the dashed line shows the distribution with the CLT applied, See how the dashed line is almost like a normal bell curve distribution?

The central limit theorem also applies to discrete random variables.

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