Exam 8: Probability Distributions and Statistics

The probability that an airplane engine will fail in a transcontinental flight is 0.002. Assuming that engine failures are independent of each other, what is the probability that, on a certain transcontinental flight, a four-engine plane will experience exactly one engine failure? Round the answer to six decimal places, if necessary. __________ What is the probability that a four-engine plane will experience exactly two engine failure? Round the answer to six decimal places, if necessary. __________ What is the probability that a four-engine plane will experience more than two engine failures? (Note: In this event, the airplane will crash!) Round the answer to nine decimal places, if necessary. _________

If the probability that a certain tennis player will serve an ace is , what is the probability that he will serve exactly four aces out of five serves?

Find the variance of the probability distribution for the histogram:

Because of late cancellations, Neptune Lines, an operator of cruise ships, has a policy of accepting more reservations than there are accommodations available. From experience, 8% of the bookings for the 90-day around-the-world cruise on the S.S. Drion, which has accommodations for 2,000 passengers, are subsequently canceled. If the management of Neptune Lines has decided, for public relations reasons, that a person who has made a reservation should have a probability of 0.90 of obtaining accommodation on the ship, determine the largest number of reservations that should be taken for a cruise on the S.S. Drion. Round your answer to the nearest integer.

The medical records of infants delivered at Kaiser Memorial Hospital show that the infants' lengths at birth (in inches) are normally distributed with a mean of 20 and a standard deviation of 2.6. Find the probability that an infant selected at random from among those delivered at the hospital measures. Round your answers to four decimal places, if necessary.

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. ​ X = The number of boys in a two-child family

Suppose X is a normal random variable with and . Find the value of .

Suppose X is a normal random variable with and . Round the answers to four decimal places, if necessary. Find the value of . __________ Find the value of . __________ Find the value of . __________

Use the appropriate normal distribution to approximate the resulting binomial distribution. Bearings is the principal supplier of ball bearings for the Sperry Gyroscope Company. It has been determined that 6% of the ball bearings shipped are rejected because they fail to meet tolerance requirements. What is the probability that a shipment of 200 ball bearings contains more than 14 rejects?

A coin is tossed four times. Let the random variable X denote the number of heads that occur. Let H denotes the outcome "heads" and T denotes the outcome "tails". Find the value assigned to each outcome of the experiment by the random variable X. ​

Use the appropriate normal distribution to approximate the resulting binomial distribution. Round your answers to four decimal places. A marksman's chance of hitting a target with each of his shots is 60%. If he fires 30 shots, what is the probability of his hitting the target

Find the value of the probability of the standard normal variable Z corresponding to the area .

Find the variance of the probability distribution for the histogram:

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The number of defective watches in a sample of six watches.

If a player placed a $8 bet on red and a $5 bet on black in a single play in American roulette, what would be the expected value of his winnings? Round your answer to the nearest cent.

During the first year at a university that uses a 4-point grading system, a freshman took ten 3-credit courses and received one As, four Bs, three Cs, and two D. Compute this student's grade point average. __________ Let the random variable X denote the number of points corresponding to a given letter grade. Find the probability distribution of the random variable X and compute E(X), the expected value of X. E(X) = __________

The birthrates in the country for the years 1981-1990 are: (The birthrate is the number of live births/1,000 population.) Compute the mean, variance, and standard deviation of the random variable X.

Let Z be the standard normal variable. Round your answers to the nearest tenth. ​ Find the value of z if z satisfies: ​ __________ ​ Find the value of z if z satisfies: ​ __________

The IQs of students at Wilson Elementary School were measured recently and found to be normally distributed with a mean of 100 and a standard deviation of 15. What the probability that a student selected at random will have IQ. Round your answers to four decimal places, if necessary.

Use the formula to determine the probability of the given event. Round the answer to four decimal places, if necessary. The probability of at least three successes in nine trials of a binomial experiment in which p = The probability is __________.