# Question: A soft drink vending machine can be regulated so that

A soft drink vending machine can be regulated so that it dispenses an average of m oz of soft drink per cup.

a. If the ounces dispensed per cup are normally distributed with a standard deviation of 0.2 oz, find the setting for m 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 cups of soft drink from the machine (set using your answer to part a).

MINITAB

Use the Calculate RANDOM DATA commands on page 283, replacing n with 40, store in with C1, mean with the value cal-culated in part a, and standard deviation with 0.2.

Use the HISTOGRAM commands on page 53 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 283, 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 291, 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 pages 53-54 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 283, 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 54 for the data in L1, entering 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 m is going to work? Explain.

FYI Repeat part b a few times. Try a different value for part a and repeat part b. Observe how many cups would overflow in each set of 40.

a. If the ounces dispensed per cup are normally distributed with a standard deviation of 0.2 oz, find the setting for m 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 cups of soft drink from the machine (set using your answer to part a).

MINITAB

Use the Calculate RANDOM DATA commands on page 283, replacing n with 40, store in with C1, mean with the value cal-culated in part a, and standard deviation with 0.2.

Use the HISTOGRAM commands on page 53 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 283, 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 291, 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 pages 53-54 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 283, 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 54 for the data in L1, entering 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 m is going to work? Explain.

FYI Repeat part b a few times. Try a different value for part a and repeat part b. Observe how many cups would overflow in each set of 40.

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