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A fair bet at craps
Almost all bets made at gambling casinos favor the house. In other words, the difference between the amount bet and the mean of the distribution of the payoff is a positive number. An exception is "taking the odds" at the game of craps, a bet that a player can make under certain circumstances. The bet becomes available when a shooter throws a 4, 5, 6, 8, 9, or 10 on the initial roll. This number is called the "point"; when a point is rolled, we say that a point has been established. If a 4 is the point, an odds bet can be made that wins if a 4 is rolled before a 7 is rolled. The probability of winning this bet is 0.5 and the payoff for a $10 bet is $20. The same probability of winning and payoff apply for an odds bet on a 10. For an initial roll of 5 or 9, the odds bet has a winning probability of 2/3 and the payoff for a $10 bet is $15. Similarly, when the initial roll is 6 or 8, the odds bet has a winning probability of 5/6 and the payoff for a $10 bet is $12. Find the mean of the payoff distribution for each of these bets. Then con?rm that the bets are fair by showing that the difference between amount bet and the mean of the distribution of the payoff is zero.
The length of a particular telemarketing phone call, x, has an exponential distribution with mean equal to 1.5 minutes.
Which of these best approximates the probability that a flight will land between 40 and 45 minutes late? .071 .284 .375 .643 .929.
Conduct the most appropriate hypothesis test using a 0.05 significance level to determine if there is a statistically significant difference between the reading of both instruments.
A pediatrician is interested in studying the effect of Motrin on reducing temperature in young children. Four children with influenza have their temperatures taken immediately before and then 20 minutes after taking a standard dose
To estimate p, we use the proportion p-hat in the sample who answer "Yes." Justify the use of a normal approximation and find the following probabilities.
provide a different example for each of the following types of variables from your work or home lifea a nominal level
What if the number of debilitating network viruses detected in a day at the firewalls of an Internet service provider within a certain geographic region is fueling a possible management decision to upgrade the detection system.
after finishing the competition in 24th place you have a little extra spending money to have fun with in vegas.
If measurements are made instead on 4 separate days and the mean result is compared with the criterion 3.5, what is the probability that Judy is diagnosed as hypokalemic?
collect cumulative data for all u.s. major carriers for the time period of january 2006 through december 2012. the data
Population blood pressure (BP) of patients is normally distributed, with a mean of 127, and standard deviation of 8. A random sample of 49 patients in the hospital found an average BP of 125.
james w. has a portfolio that includes 20 shares of disney and 30 shares of amazon. the price of disney stock is
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