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Chapter 4: Q.64 (page 287)
X ~ _____(_____,_____)
The required value is.
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Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status.
What is the standard deviation?
Sixty-five percent of people pass the state driver鈥檚 exam on the first try. A group of individuals who have taken the driver鈥檚 exam is randomly selected. Give two reasons why this is a binomial problem.
It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. What is the probability that we must survey just one or two residents until we find a California resident who does not have adequate earthquake supplies?
e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies?
f. How many California residents do you expect to need to survey until you find a California resident who does not have adequate earthquake supplies?
g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?
Find the probability that Javier volunteers for at least one event each month.
There are two similar games played for Chinese New Year and Vietnamese New Year. In the Chinese version, fair dice with numbers 1, 2, 3, 4, 5, and 6 are used, along with a board with those numbers. In the Vietnamese version, fair dice with pictures of a gourd, fish, rooster, crab, crayfish, and deer are used. The board has those six objects on it, also. We will play with bets being \(1. The player places a bet on a number or object. The 鈥渉ouse鈥� rolls three dice. If none of the dice show the number or object that was bet, the house keeps the \)1 bet. If one of the dice shows the number or object bet (and the other two do not show it), the player gets back his or her \(1 bet, plus \)1 profit. If two of the dice show the number or object bet (and the third die does not show it), the player gets back his or her \(1 bet, plus \)2 profit. If all three dice show the number or object bet, the player gets back his or her \(1 bet, plus \)3 profit. Let X = number of matches and Y = profit per game.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. List the values that Y may take on. Then, construct one PDF table that includes both X and Y and their probabilities.
e. Calculate the average expected matches over the long run of playing this game for the player.
f. Calculate the average expected earnings over the long run of playing this game for the player
g. Determine who has the advantage, the player or the house.
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