9% of all Americans live in poverty. If 36 Americans are randomly selected, find the probability that a. Exactly 3 of them live in poverty. b. At most 3 of them live in poverty. c. At least 5 of them live in poverty. d. Between 2 and 10 (including 2 and 10) of them live in poverty. 74% of all Americans live in cities with population greater than 100,000 people. If 49 Americans are randomly selected, find the probability that a. Exactly 35 of them live in cities with population greater than 100,000 people. b. At most 35 of them live in cities with population greater than 100,000 people. c. At least 36 of them live in cities with population greater than 100,000 people. d. Between 29 and 33 (including 29 and 33) of them live in cities with population greater than 100,000 people. 77% of all students at a college still need to take another math class. If 36 students are randomly selected, find the probability that a. Exactly 27 of them need to take another math class. b. At most 27 of them need to take another math class. c. At least 29 of them need to take another math class. d. Between 24 and 31 (including 24 and 31) of them need to take another math class. 55% of all Americans are home owners. If 37 Americans are randomly selected, find the probability that a. Exactly 19 of them are are home owners. b. At most 20 of them are are home owners. c. At least 20 of them are home owners. d. Between 18 and 25 (including 18 and 25) of them are home owners. The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 500 tickets. There is one $3,000 grand prize, two $500 second prizes, and fifteen $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent. Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $20. If you roll a 3, 4 or 5, you win $4. Otherwise, you pay $7. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table X P(X) b. Find the expected profit. $ (Round to the nearest cent) c. Interpret the expected value. You will win this much if you play a game. This is the most likely amount of money you will win. If you play many games you will likely win on average very close to $3.00 per game. d. Based on the expected value, should you play this game? Yes, because you can win $20.00 which is greater than the $7.00 that you can lose. No, since the expected value is negative, you would be very likely to come home with less money if you played many games. No, this is a gambling game and it is always a bad idea to gamble. Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. Yes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
9% of all Americans live in poverty. If 36 Americans are randomly selected, find the probability that
a. Exactly 3 of them live in poverty.
b. At most 3 of them live in poverty.
c. At least 5 of them live in poverty.
d. Between 2 and 10 (including 2 and 10) of them live in poverty.
74% of all Americans live in cities with population greater than 100,000 people. If 49 Americans are randomly selected, find the probability that
a. Exactly 35 of them live in cities with population greater than 100,000 people.
b. At most 35 of them live in cities with population greater than 100,000 people.
c. At least 36 of them live in cities with population greater than 100,000 people.
d. Between 29 and 33 (including 29 and 33) of them live in cities with population greater than 100,000 people.
77% of all students at a college still need to take another math class. If 36 students are randomly selected, find the probability that
a. Exactly 27 of them need to take another math class.
b. At most 27 of them need to take another math class.
c. At least 29 of them need to take another math class.
d. Between 24 and 31 (including 24 and 31) of them need to take another math class.
55% of all Americans are home owners. If 37 Americans are randomly selected, find the probability that
a. Exactly 19 of them are are home owners.
b. At most 20 of them are are home owners.
c. At least 20 of them are home owners.
d. Between 18 and 25 (including 18 and 25) of them are home owners.
The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 500 tickets. There is one $3,000 grand prize, two $500 second prizes, and fifteen $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $20. If you roll a 3, 4 or 5, you win $4. Otherwise, you pay $7.
a. Complete the
Probability Distribution Table
| X | P(X) |
|---|---|
b. Find the expected profit. $ (Round to the nearest cent)
c. Interpret the expected value.
- You will win this much if you play a game.
- This is the most likely amount of money you will win.
- If you play many games you will likely win on average very close to $3.00 per game.
d. Based on the expected value, should you play this game?
- Yes, because you can win $20.00 which is greater than the $7.00 that you can lose.
- No, since the expected value is negative, you would be very likely to come home with less money if you played many games.
- No, this is a gambling game and it is always a bad idea to gamble.
- Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games.
- Yes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost.
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