Assignment SOLUTION #1
Introduction to Probability and Statistics
January 28, 2010
Assignment SOLUTION #1
1. The following is a sample of prices, rounded to the nearest cent, charged per gallon of standard
unleaded gasoline in the San Francisco Bay area in June 1997.
137
,
139
,
141
,
137
,
144
,
141
,
139
,
137
,
144
,
141
,
143
,
143
,
141
Represent these data in a frequency table.
Solution
: We have that 137 appears three times, 139 appears twice, 141 appears four times, 143
appears twice, and 144 appears twice. Any graph which illustrates is is ﬁne.
2. The following are the estimated oil reserves, in billions of barrels, for four regions in the
western hemisphere.
United States
38.7
South America
22.6
Canada
8.8
Mexico
60.0
Represent these data in a pie chart.
Solution
: Basically, we have to calculate the total amount of barrels and then ﬁgure out the
percentage of the total each of the four regions represents. From the calculations below
we see that there are a total of 130.1 billion barrels and that the percentage of US, South
American, Canadian, and Mexican representatives are 29.7, 17.3, 6.7 and 46 percent
respectively. Any ﬁgure which has the pizza slices that make up the pie chart roughly
of this size for each region is correct. The calculations for this problem are done below
in
R.
> TOT<-38.7+22.6+8.8+60
> TOT
[1] 130.1
> US<-38.7/TOT
> SA<-22.6/TOT
> CANADA<-8.8/TOT
> MEXICO<-60/TOT
> US
[1] 0.2974635
> SA
[1] 0.1737125
> CANADA
[1] 0.06764028
> MEXICO
[1] 0.4611837
3. The following are the percentages of ash content in 12 samples of coal found in close proximity:
9
.
2
,
14
.
1
,
9