Use a computer to compare a random sample to the population from which the sample was drawn. Consider the normal population with mean 100 and standard deviation 16.

a. List values of x from   4 to   4 in increments of half standard deviations and store them in a column.

b. Find the ordinate (y value) corresponding to each abscissa (x value) for the normal distribution curve for N(100, 16) and store them in a column.

c. Graph the normal probability distribution curve for N(100, 16).

d. Generate a random sample of 100 simulated values from the N(100, 16) distribution and store them in a column.

e. Graph the histogram of the 100 values obtained in part d using the numbers listed in part a as class boundaries.

f. Calculate other helpful descriptive statistics of the 100 values and compare the data with the expected distribution. Comment on the similarities and the differences you see.

MINITAB (Release 14)

a. Use the Make Patterned Data commands in Exercise 6.66, replacing the first value with 36, the last value with 164, and the steps with 8.
b.
Choose: Calc  Prob. Dist.  Normal Select: Probability density Enter: Mean: 100 Stand. dev.: 16 Input column: C1 Optional Storage: C2  OK

c. Use the Scatterplot commands on page 328 for the data in C1 and C2.

d. Use the Calculate RANDOM DATA commands on page 327, replacing n with 100, store in with C3, mean with 100, and standard deviation with 16.

e. Use the HISTOGRAM with Fits commands on page 61 for the data in C3. To adjust histogram, select Binning with cutpoint and cutpoint positions 36:148/8.

f. Use the MEAN and STANDARD DEVIATION commands on pages 74 and 88 for the data in C3.
Excel

a. Use the RANDOM NUMBER GENERATION Patterned Distribution commands in Exercise 6.66, replacing the first value with 36, the last value with 172, and the steps with 8.

b. Activate B1; then continue with:
Choose: Insert function fx  Statistical  NORMDIST 
OK Enter: X: (A1:A? or select ‘x value’ cells)
Mean: 100 Standard dev.: 16 Cumulative: False  OK Drag: Bottom right corner of the ordinate value box down to give other ordinates

c. Use the CHART WIZARD XY(Scatter) commands on page 329 for the data in columns A and B.

d. Activate cell C1; then use the Normal RANDOM NUMBER GENERATION commands on page 328, replacing number of random numbers with 100, mean with 100, and standard deviation with 16.

e. Use the HISTOGRAM commands on page 61 with column C as the input range and column A as the bin range

f. Use the MEAN and STANDARD DEVIATION commands on pages 74 and 88 for the data in column C.