Exam 4: Discrete Probability Distributions

The random variable x represents the number of cars per household in a town of 1000 households. Find the probability of randomly selecting a household that has between one and three cars, inclusive. Cars Households 0 125 1 428 2 256 3 108 4 83

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly nine boys in ten births.

The random variable x represents the number of cars per household in a town of 1000 households. Find the probability of randomly selecting a household that has less than two cars. Cars Households 0 125 1 428 2 256 3 108 4 83

A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the test?

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

A baseball player gets four hits during the World Series and a sports announcer claims that getting four or more hits is not unusual. Use the frequency distribution below to determine if the sports announcer is correct. Hits 0 1 2 3 4 5 6 7 Players 7 9 7 4 1 1 2 1

You observe the gender of the next 100 babies born at a local hospital. You count the number of girls born. Identify the values of n, p, and q, and list the possible values of the random variable x.

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, Three returns will contain only errors favoring the taxpayer?

Find the variance of the binomial distribution for which n = 800 and p = 0.87.

Determine whether the distribution represents a probability distribution. If not, identify any requirements that are not satisfied. () 3 -0.3 6 0.5 9 0.1 12 0.3 15 0.4

According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the mean and standard deviation of the Number that never married?

Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 250 babies born at a local hospital. The random variable represents the number of girls.

A company ships computer components in boxes that contain 10 items. Assume that the probability of a defective computer component is 0.1. Use the geometric mean to find the mean number of defective parts. Interpret the results.

At a raffle, 10,000 tickets are sold at $10 each for three prizes valued at $4,800, $1,200, and $400. What is the expected value of one ticket?

State whether the variable is discrete or continuous. The height of a player on a basketball team

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Suppose that 500 couples each have a baby; find the mean and standard deviation for the number of girls in the 500 babies.

State whether the variable is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic

A mail-order company receives an average of five orders per 500 solicitations. If it sends out 100 advertisements, find the probability of receiving at least two orders. Use the Poisson distribution.

State whether the variable is discrete or continuous. The number of goals scored in a soccer game

A sports analyst records the winners of NASCAR Winston Cup races for a recent season. The random variable x represents the races won by a driver in one season. Use the frequency distribution to construct a probability distribution. Wins 1 2 3 4 5 6 7 Drivers 12 2 0 2 0 0 1