14.25 Hot Spot. Hot Spot is a California lottery game. Players pick 1 to 10 Spots (sets of numbers, each from 1 to 80) that they want to play per draw. For example, if you select a 4 Spot, you play four numbers. The lottery draws 20 numbers, each from 1 to 80. Your prize is based on how many of the numbers you picked C 27% Page 1584 of 6452 Location match one of those selected by the lottery. The odds of winning depend on the number of Spots you choose to play. For example, the overall odds of winning some prize in 4 Spot is approximately 0.256. You decide to play the 4 Spot game and buy 5 tickets. Let X be the number of tickets that win some prize. 6452 Location 18277 of 68468 32F Mostly cloudy 6:10 3/7/2 a. X has a binomial distribution. What are n and p? b. What are the possible values that X can take? e. Find the probability of each value of X. Draw a probability histogram for the distribution of X. (See Figure 142 on page 331 for an example of a probability histogram.) d. What are the mean and standard deviation of this distribution? Mark O Page 1585 the location of the mean on your histogram. 14.26 Roulette-Betting on Red. A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black. The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully 32F Mostly cloudy