1. A potato chip manufacturer was having problems with the weights and Measures
inspector after the inspectors found some bags containing less than the required
42.5 grams (formerly 1.5 ounces) of chips. In response, the manufacturer had
increased the weigh setting on the bagging machines to 50 grams, but were now
over packing the bags and giving away chips.
A random sample of bags were taken off the line and the chips in the bags were
carefully weight, as shown below:
Sample of Chip
Weights (grams)
44.32
48.42
47.86
54.24
47.67
49.26
55.06
47.87
45.80
49.22
51.09
49.97
43.39
51.95
47.86
44.85
53.83
48.24
43.64
48.79
54.42
54.66
57.57
48.94
55.33
48.05
52.67
48.55
51.98
48.86
A-What is the average weight of chips in a bag?
B-What is the standard deviation of the chip weights?
C-According to the three rule of thumb, how many bags per 1,000 are expected to be
below the required minimum weight of 42.5 grams?
D-Plot a histogram of the chip weights. Does the data appear to be well
approximated by a normal distribution?
E-Using the normal distribution approximation, how many bags per 1,000 are
expected to be below the required minimum weight of 42.5 grams?
F-What setting (mean chip weight) should be used to ensure that “almost all” the
bags contain at least 42.5 grams of chips while minimizing the excess chips in the
bags?
2.A package goods supplier designed a new package (“white”) that it thought was
more appealing than its old package (“blue”). It conducted a 10-weektrial of the two
packages in selected “matched” stores with the results shown below (sales in
thousands of dollars).
Week
1
2
3
4
5
6
7
8
9
10
Container Color
Blue
8.4
4.9
3.3
6.9
9.3
8.7
5.3
3.4
6.9
7.9
White
9.2
5.3
3.1
7.6
9.2
9.2
5.7
4.4
7.8
8.5
A-Is there any statistical evidence that one or the other package leads to higher
sales?
