a. Find the mean and standard deviation of x for a binomial probability distribution with n  16 and p  0.5.

b. Use a computer to construct the probability distribution and histogram for the binomial probability experiment with n  16 and p  0.5.

c. Use a computer to randomly generate 200 samples of size 25 from a binomial probability distribution with n  16 and p  0.5. Calculate the mean of each sample.

d. Construct a histogram and find the mean and standard deviation of the 200 sample means.

e. Compare the probability distribution of x found in part b and the frequency distribution of x in part

d. Does your information support the CLT? Explain.

MINITAB (Release 14)

a. Use the MAKE PATTERNED DATA commands in Exercise 6.66 on page 336, replacing the first value with 0, the last value with 16, and the steps with 1. Use the BINOMIAL PROBABILITY DISTRIBUTIONS commands on page 292, replacing n with 16, p with 0.5, input column with C1, and optional storage with C2. Use the Scatterplot with Connect Line commands on page 155, replacing Y with C2 and X with C1.

b. Use the BINOMIAL RANDOM DATA commands on page 303, replacing generate with 200, store in with C3–C27, number of trials with 16, and probability with 0.5. Use the ROW STATISTICS commands for a mean on page 368, replacing input variables with C3–C27 and store result in with C28. Use the HISTOGRAM commands on page 61 for the data in C28. To adjust histogram, select Binning with midpoints. Use the MEAN and STANDARD DEVIATION commands on pages 74 and 88 for the data in C28.

Excel

a. Input 0 through 16 into column A. Continue with the binomial probability commands on page 292, using n  16 and p  0.5. Activate columns A and B; then continue with:

Choose: Chart Wizard  Column  1st picture  Next 

Series Choose: Series 1  Remove Enter: Category (x)axis labels: (A1:A17 or select ‘x value’ cells)

Choose: Next  Finish

b. Use the Binomial RANDOM NUMBER GENERATION commands from Exercise 5.97 on page 304, replacing number of variables with 25, number of random numbers with 200, p value with 0.5, number of trials with 16, and output range with C1. Activate cell BB1. Use the AVERAGE INSERT FUNCTION commands in Exercise 7.13b on page 368, replacing Number1 with C1:AA1.

c. Use the RANDOM NUMBER GENERATION Patterned Distribution commands in Exercise 6.66 on page 336, replacing the first value with 6.8, the last value with 9.2, the steps with 0.4, and the output range with CC1. Use the HISTOGRAM commands on page 61 with column BB as the input range and column CC as the bin range. Use the MEAN and STANDARD DEVIATION commands on pages 74 and 88 for the data in column BB.