Exam 4: Discrete Random Variables

Solve the problem. Round to four decimal places. -We believe that 86% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 32 students from the Population and observed fewer than five in our sample who consider statistics to be an exciting Subject. Make an inference about the belief that 86% of the students consider statistics to be an Exciting subject.

Solve the problem. Round to four decimal places. -According to a recent study, 1 in every 7 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and asked Each whether she has been a victim of domestic abuse at some point in her life. Find the probability That at least 2 of the women sampled have been the victim of domestic abuse. Round to six decimal Places.

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.1. Find the probability that exactly three accidents will occur On this stretch of road each of the next two months.

Solve the problem. Round to four decimal places. -It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students And ask if they have a tattoo. Use a binomial probability table to find the probability that exactly 5 Of the students reported that they did have at least one tattoo.

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 $610 profit per policy sold?

A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.4 0.25 0.35 Suppose the mean cost of the frogs is $\$ 12.38$ per week. Interpret this value.

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 8.5. Interpret the value of the mean.

The hypergeometric random variable x counts the number of successes in the draw of n elements from a set of N elements containing r successes.

Which binomial probability is represented on the screen below?

Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac)from the local paint store in order to paint his motherʹs house. Unknown to the man, three of these cans contains An incorrect mix of paint. For this weekendʹs big project, the man randomly selects four of these 1-gallon cans to paint his motherʹs living room. Let x = the number of the paint cans selected that Are defective. Unknown to the man, x follows a hypergeometric distribution. Find the probability That at least one of the four cans selected contains an incorrect mix of paint.

Solve the problem. Round to four decimal places. -If x is a binomial random variable, compute p(x)for n = 5, x = 3, q = 0.2.

Compute $\left( \begin{array} { l } 9 \\ 4 \end{array} \right)$ .

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 7.4. Find the probability of observing exactly four accidents on This stretch of road next month.

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.

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 6.1. Find the probability that fewer than three accidents will Occur next month on this stretch of road.

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 wonʹt is 0.30.

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. How Many of the sampled voters do we expect to vote in the next presidential election?

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 7. Find the probability that exactly six babies will be born during a particular 1-hour Period at this hospital.

It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students And ask if they have a tattoo. Find the standard deviation for this binomial random variable. Round to the nearest hundredth when necessary.

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