Exam 4: Discrete Probability Distributions

An insurance actuary asked a sample of senior citizens the cause of their automobile accidents over a two -year period. The random variable x represents the number of accidents caused by their failure to yield the right of way. Use the frequency distribution to construct a probability distribution. Accidents 0 1 2 3 4 5 Senior Citizens 4 3 12 3 2 1

A book contains 500 pages. If there are 200 typing errors randomly distributed throughout the book, use the Poisson distribution to determine the probability that a page contains exactly two errors.

Decide which probability distribution -binomial, geometric, or Poisson- applies to the question. You do not need to answer the question. -Given: The probability that a federal income tax return is filled out incorrectly with an error in favor of the taxpayer is 20%. Question: What is the probability that of the ten tax returns randomly selected for an audit in A given week, three returns will contain only errors favoring the taxpayer?

Thirty-eight percent of people in the United States have type O+ blood. You randomly select 30 Americans and ask them if their blood type is O+. Identify the values of n, p, and q, and list the possible values of the random variable x.

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizens are chosen, what is the mean number favoring the substation?

Find the standard deviation of the binomial distribution for which n = 1000 and p = 0.94.

The probability that an individual is left-handed is 0.12. In a class of 39 students, what is the probability of finding five left-handers?

State whether the variable is discrete or continuous. The blood pressures of a group of students the day before their final exam

A sales firm receives an average of three calls per hour on its toll-free number. For any given hour, find the probability that it will receive at least three calls. Use the Poisson distribution.

Find the mean of the binomial distribution for which n = 40 and p = 0.2.

A test consists of 100 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers.

Thirty percent of voters think that Congress should help write standards for school food. You randomly select eight voters and ask them whether Congress should help write standards for school food. The random variable represents the number of voters who think that Congress should help write standards for school food. Graph the binomial distribution using a histogram and describe its shape.

One thousand tickets are sold at $2 each. One ticket will be randomly selected and the winner will receive a color television valued at $387. What is the expected value for a person that buys one ticket?

An airline has a policy of booking as many as 150 persons on a plane that seats 140. Past studies indicate that only 85% of booked passengers show up for their flight. Find the probability that if the airline books 150 persons for a 140-seat plane, not enough seats will be available.

Determine whether the distribution represents a probability distribution. If not, identify any requirements that are not satisfied. () 1 1.2 2 1.2 3 1.4 4 1.1 5 1.1

A local fire station receives an average of 0.55 rescue calls per day. Use the Poisson distribution to find the probability that on a randomly selected day, the fire station will receive fewer than two calls.

A sales firm receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly nine calls. Use the Poisson distribution.

From the probability distribution, find the mean and standard deviation for the random variable x, which represents the number of cars per household in a town of 1000 households. () 0 0.125 1 0.428 2 0.256 3 0.108 4 0.083

State whether the variable is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

In a raffle, 1,000 tickets are sold for $2 each. One ticket will be randomly selected and the winner will receive a laptop computer valued at $1200. What is the expected value for a person that buys one ticket?