Exam 5: Discrete Probability Distributions

A survey asked 874 people how many times per week they dine out at a restaurant. The results are presented in the following table. Number of Times Frequency 0 122 1 272 2 221 3 116 4 80 5 30 6 25 7 8 Total 874 Consider the 874 people to be a population. Let $X$ be the number of times per week a person dines out for a person sampled at random from this population. Compute the mean.

Determine whether the random variable described is discrete or continuous. The number of 3-point shots made in a basketball game

Last year, a manufacturer produced 450,000 DVD players. Of these, approximately $4 \%$ were defective. Assume that a simple random sample of $n = 170$ players is drawn. Use the Poisson approximation to the binomial distribution to compute the probability that exactly fourteen of the 170 DVD players were defective.

A student takes a true-false test that has 13 questions and guesses randomly at each answer. Let $X$ be the number of questions answered correctly. Find $P ( 5 )$

A multiple choice quiz consists of 100 questions, each with 5 possible answers. Find the mean for the number of correct answers, if a student guesses on each question.

The formula for the variance of a probability distribution is .

A survey asked 851 people how many times per week they dine out at a restaurant. The results are presented in the following table. Number of Times Frequency 0 104 1 244 2 242 3 142 4 62 5 22 6 27 7 8 Total 851 Consider the 851 people to be a population. Let $X$ be the number of times per week a person dines out for a person sampled at random from this population. Find the probability that a person does not dine out at all.

Compute the probability of X successes. n = 5, X = 4, p = 0.7

A bag contains 30 white marbles and 30 black marbles. If 8 marbles are chosen, what is the probability that there will be 2 white marbles and 6 black marbles?

Find the variance for the values of $n$ and $p$ when the conditions for the binomial distributi are met. $n = 500 , p = 0.75$

An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.05 of a $20,000 loss, probability 0.2 of a $20,000 profit, Probability 0.15 of a $35,000 profit, and probability 0.6 of breaking even (a profit of $0). What is the expected value of the profit?

Determine the indicated probability for a binomial experiment with the given number of trials $n$ and the given success probability $p$ . $n = 12 , p = 0.7 , P \text { (3 or fewer) }$

If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices.

A school club consists of 26 male students and 11 female students. If 4 students are selected to represent the club in the student government, what is the probability Male and 2 will be female?

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 40% of adult Australian sheep dogs weigh 65 pounds or more. A sample Of 14 adult dogs is studied. What is the standard deviation of the number of dogs who Weigh 65 lb or more?

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 3 per milliliter. Find the mean Number of bacteria in a 4-milliliter sample.

In a large bag of marbles, 25% of them are red. A child chooses 4 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets exactly Three red marbles?

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 4 per milliliter. Find the standard Deviation of the number of bacteria in a 6-milliliter sample.

Using the probability distribution listed, the mean would be 1.6 . 0 1 2 3 ( ) 0.2 0.1 0.3 0.4

Determine whether the random variable described is discrete or continuous. The length in seconds of a randomly-selected TV commercial