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A binomial probability experiment is conducted with the given parameters. Compute the probability of \(x\) success in the \(n\) independent trials of the experiment. \(n=15, p=0.85, x=12\)

A binomial probability experiment is conducted with the given parameters. Compute the probability of \(x\) success in the \(n\) independent trials of the experiment. \(n=12, p=0.35, x \leq 4\)

(a) construct a binomial probability distribution with the given parameters; (b) compute the mean and standard deviation of the random variable using the methods of Section 6.1; (c) compute the mean and standard deviation, using the methods of this section; and (d) draw the probability histogram, comment on its shape, and label the mean on the histogram. \(n=6, p=0.3\)

Suppose a life insurance company sells a \(\$ 250,000\) one-year term life insurance policy to a 20 -yearold male for \(\$ 350 .\) According to the National Vital Statistics Report, Vol. \(53,\) No. \(6,\) the probability that the male survives the year is \(0.998611 .\) Compute and interpret the expected value of this policy to the insurance company.

(a) construct a binomial probability distribution with the given parameters; (b) compute the mean and standard deviation of the random variable using the methods of Section 6.1; (c) compute the mean and standard deviation, using the methods of this section; and (d) draw the probability histogram, comment on its shape, and label the mean on the histogram. \(n=9, p=0.75\)

In the game of roulette, a player can place a \(\$ 5\) bet on the number 17 and have a \(\frac{1}{38}\) probability of winning. If the metal ball lands on \(17,\) the player wins \(\$ 175\) Otherwise, the casino takes the player's \(\$ 5 .\) What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?

In the Cash Five Lottery in Connecticut, a player pays \(\$ 1\) for a single ticket with five numbers. Five Ping-Pong balls numbered 1 through 35 are randomly chosen from a bin without replacement. If all five numbers on a player's ticket match the five chosen, the player wins \(\$ 100,000 .\) The probability of this occurring is \(\frac{1}{324,632} .\) If four numbers match, the player wins \(\$ 300 .\) This occurs with probability \(\frac{1}{2164^{\circ}}\). If three numbers match, the player wins \(\$ 10 .\) This occurs with probability \(\frac{1}{75} .\) Compute and interpret the expected value of the game from the player's point of view.

(a) construct a binomial probability distribution with the given parameters; (b) compute the mean and standard deviation of the random variable using the methods of Section 6.1; (c) compute the mean and standard deviation, using the methods of this section; and (d) draw the probability histogram, comment on its shape, and label the mean on the histogram. \(n=9, p=0.8\)

On-Time Flights According to American Airlines, its flight 215 from Orlando to Los Angeles is on time \(90 \%\) of the time. Suppose 15 flights are randomly selected and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Find the probability that exactly 14 flights are on time. (c) Find the probability that at least 14 flights are on time. (d) Find the probability that fewer than 14 flights are on time. (e) Find the probability that between 12 and 14 flights, inclusive, are on time.

Some standardized tests, such as the SAT test, incorporate a penalty for wrong answers. For example, a multiple-choice question with five possible answers will have 1 point awarded for a correct answer and \(\frac{1}{4}\) deducted point for an incorrect answer. Questions left blank are worth 0 points. (a) Find the expected number of points received for a multiple-choice question with five possible answers when a student just guesses. (b) Explain why there is a deduction for wrong answers.