# Hw1Sol - SIEO 3600(IEOR Majors Introduction to Probability...

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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

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## This note was uploaded on 10/03/2011 for the course SIEO W3600 taught by Professor Yunanliu during the Spring '10 term at Columbia.

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Hw1Sol - SIEO 3600(IEOR Majors Introduction to Probability...

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