# Suppose X,n} is a sequence of random variables draw from an underlying popu-lation space, then the sample mean of {Xn} defined as Xnin distribution to Normal Distribution N(u, a2), where u E[X3], o2:E1Xi, convergeVar[X Plot the histogram of 2000 sample mean X10 together with N(20, 2). Whatis your conclusion from the graph.

Question
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Step 1

From the given information, the sample mean X10-bar follows normal distribution N(20, 25/10).

That is, µ=20 and

Step 2

Generating 2000 sample means from the normal distribution with mean 20 and the standard deviation 1.58.

Excel Procedure:

1. Go to Data
2. Click on Data Analysis.
3. Select ‘Random number generation’ and click on ‘OK’.
4. Enter 1 for ‘Number of variables’.
5. Enter 2000 for ‘Number of random numbers’.
6. Select ‘Normal’ under ‘Distribution’.
7. Enter 20 for mean.
8. Enter 58 for standard deviation.
9. Click on ‘OK’.

Excel Output:

Here, there are more number of samples. Therefore, entire samples cannot be displayed:

Step 3

The histogram is constructed below:

Steps to construct box plot:

• Select the 2000 random numbers.
• Go to Insert.
• Select histogram under ...

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