Exam 4: Discrete Random Variables

A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Which of the following is necessary for this problem to be analyzed using the binomial random variable? I. There are two outcomes possible for each of the 20 voters sampled. II. The outcomes of the 20 voters must be considered independent of one another. III. The probability a voter will actually vote is 0.70, the probability they won't is 0.30. A) I only B) II only C) III only D) I, II, and III

If x is a binomial random variable, calculate σ for n = 100 and p = 0.3. Round to three decimal places when necessary.

A binomial random variable is defined to be the number of units sampled until x successes is observed.

The number of homeruns hit during a major league baseball game follows a Poisson distribution with a mean of 3.2. Find the probability that a randomly selected game would have exactly 5 homeruns hit.

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7.7. Find the probability that fewer than three accidents will occur next month on this stretch of road.

A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 42% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?

Consider the given discrete probability distribution. Find P(x = 1 or x = 2). x 0 1 2 3 4 5 p(x) .30 .25 .20 .15 .05 .05

The conditions for both the hypergeometric and the binomial random variables require that each trial results in one of two outcomes.

A literature professor decides to give a 15-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than .10. What score should be set as the lowest passing grade?

In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random variable. x (x) 0 .30 1 .40 2 .20 3 .06 4 .04

The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 8.9. Find the probability that exactly four tickets are written on a randomly selected day.

A local bakery has determined a probability distribution for the number of cheesecakes it sells in a given day. The distribution is as follows: Number sold in a day 0 5 10 15 20 Prob (Number sold) 0.14 0.16 0.23 0.17 0.3 Find the number of cheesecakes that this local bakery expects to sell in a day.

Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men are selected to fill the appointed positions.