Exam 4: Discrete Random Variables

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 1 0 1 2 3 p(x) .1 .2 .3 .3 .1

According to a published study, 1 in every 6 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.

Management at a home improvement store randomly selected 120 customers and observed their shopping habits. They recorded the number of items each of the customers purchased as well as The total time the customers spent in the store. Identify the types of variables recorded by the Managers of the home improvement store.

A bank offers online banking to its customers free of charge. While online, customers can also sign up for additional services that the bank offers. Let $x$ be the number of customers who sign up for additional services online each day. Suppose the distribution of $x$ is approximated well by a Poisson distribution with mean $\lambda = 42.3$ . Find $E ( x )$ and interpret its value.

Consider the given discrete probability distribution. Find the probability that x equals 5.

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

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?

The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 4 goals per game. Find the probability that the team scored exactly seven goals in Each of two randomly selected games.

The number of goals scored at each game by a certain hockey team follows a Poisson distribution with a mean of 6 goals per game. Find the probability that the team will score more than three Goals during a game.

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 1 3 5 7 9 p(x) .1 .1 .2 .1 .2

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

Compute $\left( \begin{array} { l } 5 \\ 4 \end{array} \right)$ .

Suppose a Poisson probability distribution with $\lambda = 2.6$ provides a good approximation of the distribution of a random variable $x$ .. Find $\mu$ for $x$ .

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

We believe that 81% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 39 students from the Population. How many of the sampled students do we expect to consider statistics to be an Exciting subject?

You randomly select 7 students from a class with 15 male and 20 female students. What is the probability that you will choose exactly 4 females?

Classify the following random variable according to whether it is discrete or continuous. The number of cups of coffee sold in a cafeteria during lunch

Classify the following random variable according to whether it is discrete or continuous. The speed of a car on a Los Angeles freeway during rush hour traffic

A local newspaper claims that $70 \%$ of the items advertised in its classifieds section are sold within 1 week of the first appearance of the ad. To check the validity of the claim, the newspaper randomly selected $n = 25$ advertisements from last year's classifieds and contacted the people who placed the ads. They found that 14 of the 25 items sold within a week. Based on the newspaper's claim, is it likely to observe $x \leq 14$ who sold their item within a week? Use a binomial probability table.

Calculate the mean for the discrete probability distribution shown here. X 1 6 8 10 P(X) 0.02 0.2 0.06 0.72