Exam 4: Discrete Random Variables

An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 2002 compact model are defective. If 14 of these cars are independently sampled, what is the probability that more than half need new gas tanks?

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability that the random variable x is a value greater than 5. 2 3 5 8 10 () 0.10 0.20 0.30 0.30 0.10

Classify the following random variable according to whether it is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska

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

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7.2. Find the probability that exactly five accidents will occur on this stretch of road each of the next two months.

About 40% of the general population donate time and energy to community projects. Suppose 15 people have been randomly selected from a community and each asked whether he or she donates time and energy to community projects. Let x be the number who donate time and energy to community projects. Use a binomial probability table to find the probability that more than five of the 15 donate time and energy to community projects.

Consider the given discrete probability distribution. Construct a graph for p(x). x 1 2 3 4 5 6 p(x) .30 .25 .20 .15 .05 .05

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. Use a binomial probability table to find the probability that more than 12 of the eligible voters sampled will vote in the next presidential election.

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

The conditions for both the hypergeometric and the binomial random variables require that the trials are independent.

Given that x is a hypergeometric random variable with N = 15, n = 6, and r = 10, compute P(x = 0).

If x is a binomial random variable, compute p(x) for n = 5, x = 1, q = 0.8.

An automobile insurance company estimates the following loss probabilities for the next year on a $25,000 sports car: Total loss: 0.001 50\% loss: 0.01 25\% loss: 0.05 10\% loss: 0.10 No loss: 0.839 Assuming the company will sell only a $500 deductible policy for this model (i.e., the owner covers the first $500 damage), how much annual premium should the company charge in order to average $620 profit per policy sold? 2 Find Mean, Variance, Standard Deviation

According to a published study, 1 in every 4 men has been involved in a minor traffic accident. Suppose we have randomly and independently sampled twenty-five men and asked each whether he has been involved in a minor traffic accident. How many of the 25 men do we expect to have never been involved in a minor traffic accident? Round to the nearest whole number.

For a binomial distribution, if the probability of success is .48 on the first trial, what is the probability of failure on the second trial?

Consider the given discrete probability distribution. Construct a graph for p(x). x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $2.50 each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $3 each, find the probability distribution for her daily profit. A) Profit P (profit) -\ 200 .5 -\ 50 .25 \ 100 .25 B) Profit P (profit) \ 300 .5 \ 450 .25 \ 600 .25 C) Profit P(profit) \ 100 .5 \ 250 .25 \ 400 .25 D) Profit P (profit) \ 50 .5 \ 75 .25 \ 100 .25

A new drug is designed to reduce a person's blood pressure. Thirteen randomly selected hypertensive patients receive the new drug. Suppose the probability that a hypertensive patient's blood pressure drops if he or she is untreated is 0.5. Then what is the probability of observing 11 or more blood pressure drops in a random sample of 13 treated patients if the new drug is in fact ineffective in reducing blood pressure? Round to six decimal places.

The school newspaper surveyed 100 commuter students and asked two questions. First, students were asked how many courses they were currently enrolled in. Second, the commuter students were asked to estimate how long it took them to drive to campus. Considering these two variables, number of courses would best be considered a _________ variable and drive time would be considered a _________ variable.