Chapter 6: Q.72 (page 403)
Explain whether the given random variable has a binomial distribution.
Lefties Exactly of the students in a school are left-handed.
The given distributon is binomial
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Benfordโs law and fraud Refer to Exercise 13. It might also be possible to detect an employeeโs fake expense records by looking at the variability in the first digits of those expense amounts.
(a) Calculate the standard deviation ฯY. This gives us an idea of how much variation weโd expect in the employeeโs expense records if he assumed that first digits from to were equally likely.
(b) Now calculate the standard deviation of first digits that follow Benfordโs law (Exercise 5). Would using standard deviations be a good way to detect fraud? Explain.
Keno is a favorite game in casinos, and similar games are popular in the states that operate lotteries. Balls numbered to are tumbled in a machine as the bets are placed, then of the balls are chosen at random. Players select numbers by marking a card. The simplest of the many wagers available is โMark Number.โ Your payoff is on a bet if the number you select is one of those chosen. Because of numbers are chosen, your probability of winning is , or . Let the amount you gain on a single play of the game.
(a) Make a table that shows the probability distribution of .
(b) Compute the expected value of . Explain what this result means for the player
Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick game that New Hampshire shares with Maine and Vermont. You choose a number with digits from to ; the state chooses a three-digit winning number at random and pays you if your number is chosen. Because there are numbers with three digits, you have a probability of of winning. Taking to be the amount your ticket pays you, the probability distribution of is
(a) Show that the mean and standard deviation of are and .
(b) If you buy a Pick 3 ticket, your winnings are , because it costs to play. Find the mean and standard deviation of . Interpret each of these values in context.
46. Cereal A company's single-serving cereal boxes advertise ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with a mean of ounces and a standard deviation of ounces.
(a) Letthe excess amount of cereal beyond what's advertised in a randomly selected box, measured in grams ( ounce grams). Find the mean and standard deviation of .
(b) Find the probability of getting at least grams more cereal than advertised.
Explain whether the given random variable has a binomial distribution.
Lefties Exactly of the students in a school are left-handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let the number of students chosen.
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