A soft-drink vending machine can be regulated to ensure that it dispenses an average of  oz.

of soft drink per glass.

a. If the ounces dispensed per glass are normally distributed with a standard deviation of 0.2 oz., find the setting for  that will allow a 6-oz.

glass to hold (without overflowing) the amount dispensed 99% of the time.

b. Use a computer or calculator to simulate drawing a sample of 40 glasses of soft drink from the machine (set using your answer to part a).

MINITAB (Release 14)

Use the Calculate RANDOM DATA commands on page 327, replacing n with 40, store in with C1, mean with the value calculated in part

a, and standard deviation with 0.2.

Use the HISTOGRAM commands on page 61 for the data in C1. To adjust the histogram, select Binning with cutpoint and cutpoint positions 5:6.2/0.05.

Excel Use the Normal RANDOM NUMBER GENERATION commands on page 328, replacing n with 40, the mean with the value calculated in part

a, the standard deviation with 0.2, and the output range with A1.

Use the RANDOM NUMBER GENERATION Patterned Distribution on page 336, replacing the first value with 5, the last value with 6.2, the steps with 0.05, and the output range with B1.

Use the HISTOGRAM commands on page 61 with column A as the input range and column B as the bin range.
TI-83/84 Plus Use the 6:randNorm commands on page 328, replacing the mean with the value calculated in part

a, the standard deviation with 0.2, and the number of trials with 40. Store in with L1.
Use the HISTOGRAM commands on page 62 for the data in L1, entering the following WINDOW VALUES: 5, 6.2, 0.05, 1, 10, 1, 1.

c. What percentage of your sample would have overflowed the cup?

d. Does your sample seem to indicate the setting for  is going to work? Explain.
FYI Repeat part b a few times. Try a different value for the mean amount dispensed and repeat part

b. Observe how many would overflow in each set of 40.