Exam 4: Discrete Random Variables

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

Classify the following random variable according to whether it is discrete or continuous. The height of a player on a basketball team

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 fewer than two accidents will occur on this stretch of road during a month.

For a binomial distribution, if the probability of success is .63 on the first trial, what is the probability of success on the second trial?

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with λ = 4.7 alarms per year. Identify the mean and standard deviation for this distribution.

According to a recent study, 1 in every 9 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.

50 students were randomly sampled and asked questions about their exercise habits. One of the questions they were asked concerned the frequency of exercise, defined to be the number of times they exercised in a week. This variable would be characterized as which type of random variable?

The hypergeometric random variable x counts the number of successes in the draw of 3 elements from a set of 8 elements containing 4 successes. List the possible values of x.

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?

The number of homeruns hit during a major league baseball game follows a Poisson distribution with λ = 3.2. Find the mean and standard deviation for this distribution.

Suppose a Poisson probability distribution with ? = 0.8 provides a good approximation of the distribution of a random variable x.. Find ? for x.

Find the mean and standard deviation of the probability distribution for the random variable x, which represents the number of cars per household in a small town. x P(x) 0 .125 1 .428 2 .256 3 .108 4 .083

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.

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

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

The probability that an individual is left-handed is 0.16. In a class of 80 students, what is the mean and standard deviation of the number of left-handed students? Round to the nearest hundredth when necessary.

Given that x is a hypergeometric random variable, compute p(x) for N = 8, n = 5, r = 3, and x = 2.

You test 4 items from a lot of 15. What is the probability that you will test no defective items if the lot contains 3 defective items?

Given that x is a hypergeometric random variable with N = 10, n = 3, and r = 5: a. Display the probability distribution in tabular form. b. Compute μ and σ for x. c. What is the probability that x will fall within the interval μ ± 2σ

If x is a binomial random variable, calculate μ for n = 70 and p = 0.4.