Math Test I - Fall 2009: Population, Costs, Combinations, Mean, Median, Poker - Prof. John | Exams Mathematics

Paulos Math 0824/0924 - Test I - Show All Work! Fall, 2009

1a). Are there more people on Earth or teeth of Americans? About how many of each

are there?

1b). Ground beef costs 55 baht per kilogram in Thailand. If there are 36 baht to the

dollar, 2.2 pounds per kilogram, and 16 ounces in a pound, what is the cost in

pennies per ounce?

1a). 6.5 billion people versus approximately (30*300 million) or 9 billion. More

teeth. If the numbers are way, way off, take points off even if the answer is correct.

1b). If we do the transformation, we get (55 baht / kilogram) * ($1 / 36 baht) * (1

kilogram / 2.2 pounds) *

(1 pound / 16 ounce) * (100 cents/ $1) = 4.3 cents / ounce.

2a). How many possible sets of 2-letter initials (examples: FT, GR, LK, ... ) are there?

How many sets of 2-letter initials followed by two digits (examples: TY56, RR19,

KW08 ..). are there?

2b). Amityville has 80,000 people. How do you know for sure that at least two of

them are the same age and have the same 2-letter initials?

2a). By the multiplication principle there are 26*26 or 676 different ordered pairs of

initials. Also by the multiplication principle there are 26*26*10*10 or 67,600

different ordered pairs of initials followed by a two-digit number (or age).

2b.) John Smith, age 24, is JS24. Since there are more people in Amityville than there

are two-digit initials followed by ages, at least two people are the same age and have

the same initials.

3a). Assume most of the class does very well on this test, but some students get

close to zero. What would be higher, the mean score on the quiz or the median

score? Explain.

3b). Explain why almost everyone has a greater than average number of fingers.

3a). The students who score near zero will bring the mean or average down, but

won't affect the median, which will therefore be larger.

3b). Some people have only 9 or fewer fingers, so the average number of fingers is a

tiny bit under 10. Since almost everyone has 10 fingers, almost everyone has a

greater number of fingers than the average.

4a). Bill O'Reilly said it's not surprising that Canadians live longer on average than

Americans because there are 10 times as many of us and thus 10 times as many

heart attacks, accidents, etc. What's your reaction to this statement?

4b). Approximately how many seconds have you been alive?

4a). Longevity has nothing to do with population. Of course, there are more heart

attacks, accidents, etcetera in the US than there are in Canada, but that doesn't say

anything about the average age of death in the two countries. A tiny country of one

Partial preview of the text

Download Math Test I - Fall 2009: Population, Costs, Combinations, Mean, Median, Poker - Prof. John and more Exams Mathematics in PDF only on Docsity!

Paulos Math 0824/0924 - Test I - Show All Work! Fall, 2009 1a). Are there more people on Earth or teeth of Americans? About how many of each are there? 1b). Ground beef costs 55 baht per kilogram in Thailand. If there are 36 baht to the dollar, 2.2 pounds per kilogram, and 16 ounces in a pound, what is the cost in pennies per ounce? 1a). 6.5 billion people versus approximately (30300 million) or 9 billion. More teeth. If the numbers are way, way off, take points off even if the answer is correct. 1b). If we do the transformation, we get (55 baht / kilogram) * ($1 / 36 baht) * ( kilogram / 2.2 pounds) * (1 pound / 16 ounce) * (100 cents/ $1) = 4.3 cents / ounce. 2a). How many possible sets of 2-letter initials (examples: FT, GR, LK, ... ) are there? How many sets of 2-letter initials followed by two digits (examples: TY56, RR19, KW08 ..). are there? 2b). Amityville has 80,000 people. How do you know for sure that at least two of them are the same age and have the same 2-letter initials? 2a). By the multiplication principle there are 2626 or 676 different ordered pairs of initials. Also by the multiplication principle there are 262610*10 or 67, different ordered pairs of initials followed by a two-digit number (or age). 2b.) John Smith, age 24, is JS24. Since there are more people in Amityville than there are two-digit initials followed by ages, at least two people are the same age and have the same initials. 3a). Assume most of the class does very well on this test, but some students get close to zero. What would be higher, the mean score on the quiz or the median score? Explain. 3b). Explain why almost everyone has a greater than average number of fingers. 3a). The students who score near zero will bring the mean or average down, but won't affect the median, which will therefore be larger. 3b). Some people have only 9 or fewer fingers, so the average number of fingers is a tiny bit under 10. Since almost everyone has 10 fingers, almost everyone has a greater number of fingers than the average. 4a). Bill O'Reilly said it's not surprising that Canadians live longer on average than Americans because there are 10 times as many of us and thus 10 times as many heart attacks, accidents, etc. What's your reaction to this statement? 4b). Approximately how many seconds have you been alive? 4a). Longevity has nothing to do with population. Of course, there are more heart attacks, accidents, etcetera in the US than there are in Canada, but that doesn't say anything about the average age of death in the two countries. A tiny country of one

million where the average age at death was 105 would have even fewer heart attacks, cancers, etcetera. 4b). The average age in this class may be about 20, so 20 years * 365 days / year * 24 hours / day * 60 minutes / hour * 6o second / minute yields approximately 600 million seconds - 600,000,000. 5a). Can you change some of the plus signs to minus signs in order to make the sum of 1+2+3+4+5+6+7+8 equal to zero? If so, do it. If not, why not? Same question with 1+2+3+4+5+6+7+8+9? 5b). In a drawer there are 6 red, 6 blue, 6 black, and 6 white socks. You reach in and pick socks at random. What is the smallest number you need to pick so that you can be certain of getting a matching pair? What is the smallest number you need to be certain of getting a red pair? 5a). The sum of the integers from 1 to 8, determined by simply adding them or by using the formula n(n+1)/2, is 36. Since it's even if we can find a way to subtract 18 from the sum, we'll get to zero. That's not hard. One example (there are others) is 1+2+3-4+5-6+7-8 = 0. But, in the second case, the sum of the integers from 1 to 9 is 45, an odd number, so every time we change a plus x to a minus x, we subtract 2x from the sum. Since 2x is always even and an odd number minus an even number is odd, we can never achieve a sum of zero. 5b). Since there are four colors, the pigeon hole principle says that you need to pick out at least 5 socks to be certain of getting a matching pair. To be certain of getting a red pair in the worst possible case, you need to pick out 20 socks (all 6 of the white, all 6 blue, all 6 black, and 2 red). 6a). Here's an excerpt from a novel. What's wrong with the math? Four million ... heard it. Ten percent remember it. One percent of those matter. One percent of those do something about it. That's still - he does the math - four people. From: "The Betrayal", by Sabin Willett. 6b). What's odd about the claim that there are 401,347 dogs in the Philadelphia metropolitan area? 6a). The multiplication doesn't pan out since 4,000,000 * .10 * .01 * .01 = 40, not 4. 6b). It's too precise. There's no reasonable way of determining the exact number. If instead they present an argument about a different estimate for the number of dogs, you can give them a couple of points. 7a). About how many people die in car accidents in this country every day? 7b). In light of the above number, comment on a news story claiming that because of drinking and driving more than 400 people will die over the upcoming four-day holiday weekend? Is the claim surprising? 7a). About 40,000 or so per year, so 40,000/365 or 110 per year, or, more rounding off the number of days in a year, 40,000/400 or 100 per day. 7b). In any 4-day period, one might expect 4 times this number of fatal accidents to

Math Test I - Fall 2009: Population, Costs, Combinations, Mean, Median, Poker - Prof. John, Exams of Mathematics

Related documents

Partial preview of the text

Download Math Test I - Fall 2009: Population, Costs, Combinations, Mean, Median, Poker - Prof. John and more Exams Mathematics in PDF only on Docsity!