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# Suppose the random variable X is normally distributed with a mean of 20.30 and a standard deviation of 0.

Suppose the random variable X is normally distributed with a mean of 20.30 and a standard deviation of 0.55. We are going to have Minitab simulate1000 values of X as well as simulate the mean of 1000 samples of size 10. We will then compare the means, standard deviations, and shapes of these two distributions.

a. Have Minitab simulate 1000 values of X and store the 1000 values in the column c1.

To for this, click on Calc > Random Data > Normal.

In the window that opens up, click on Generate ... rows of data box and type in 1000. Then click in the Store in columns box and type c1, click in the Mean box and type 20.30, click in the Standard deviation box and type in 0.55, and click OK. o

Construct a histogram of your data such that the horizontal axis goes from 18 to 23 in increments of 0.1.

for this, click on Graph > Histogram > Simple > OK. Select c1 variable in the Graph variables section. Press OK. Double click on the horizontal axis of your histogram to open up the Edit Scale window. Click on the Binning tab, click on cutpoint, the click on Midpoint/cutpoint positions and enter 18:23/0.1. Click on OK.

o Copy and paste the histogram into a Word Document and submit with your answers

o Find the mean and standard deviation for the data. Stat > Basic Statistics > Display Descriptive Statistics. Select c1 variable in the Variables section. Press OK.

o Copy and paste the descriptive statistics into a Word Document and submit with your answers b.

We now want to simulate drawing 1000 samples of size 10 from .

for this, repeat what you did in question 1(a), but place your simulated data in columns 2 through 11. Think of the entries in row 1 of columns 2- 11 as the first sample of size 10, the entries in row 2 of columns 2-11 as the second sample of size 10, etc. Click Calc > Random Data > Normal as before. At the Normal Distribution window do everything as before, except now in the Store in columns box type c2-c11 then click OK

. o You should now have 1000 rows of data in each of columns 2 through 11. For each row, we want to compute the sample mean for the 10 values in columns 2- 11 of that row and place the sample mean in the correct row of column 12.

For this, click Calc > Row Statistics. In the Row Statistics window click Mean, in the Input variables box type c2-c11, and in the Store result box type in c12, and click OK.

o Find the mean and standard deviation for the data of c12 Stat > Basic Statistics > Display Descriptive Statistics. Select c12 variable in the Variables section. Press OK

. o The means of your 1000 repetitions of samples of size 10 should now be in column 12. Construct a histogram of your sample means using the same range of values on the horizontal axis as your graph from question 1(a)

. o Copy and paste the histogram and descriptive statistics into a Word Document and submit with your answers

Questions: What are the similarities and differences between the histogram from question (a) and that from question (b)? How do you compare the mean and standard deviation of part (a) with that of part (b)?