Exam 6: Discrete Probability Distributions

In a poll conducted by a survey firm, 75% of respondents said that their jobs were sometimes or always stressful. Nine workers are chosen at random. What is the probability that less than 4 of Them find their jobs stressful?

At an airport, 78% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that exactly 7 of them were on time.

The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. 0 1 2 3 4 5 ( ) 0.08 0.26 0.32 0.16 0.11 0.07 Find the probability that there are fewer than four people in line.

It is estimated that 30% of households own a riding lawn mower. A sample of 18 households is studied. What is the probability that no more than 3 of these own a riding lawn mower?

Determine whether the table represents a discrete probability distribution. x P(x) 5 0.5 6 0.3 7 0.5 8 -0.3

A student takes a true-false test that has 8 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(6 or more)

Compute the mean of the random variable with the given discrete probability distribution. x P(x) 0 0.2 15 0.05 25 0.45 30 0.3

Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t$ $\lambda = 0.8 , t = 3 , P ( 2 )$

In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001. What is the expected value of your profit?

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find P(1 or more). x 0 1 2 3 4 P(x) 0.09 0.63 0.18 0.07 0.03

At an airport, 78% of recent flights have arrived on time. A sample of 14 flights is studied. Find the probability that more than 12 of them were on time.

It is estimated that 40% of households own a riding lawn mower. A sample of 13 households is studied. What is the probability that more than 10 of these own a riding lawn mower?

Last year, a manufacturer produced 350,000 DVD players. Of these, approximately 1% were defective. Assume that a simple random sample of n = 140 players is drawn. Use the Poisson Approximation to the binomial distribution to compute the standard deviation of the number of DVD Players that were defective.

Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t \text {. }$ $\lambda = 0.8 , t = 4 , P ( \text { At least } 2 )$

A coin is tossed 14 times. Let X be the number of heads obtained. Is this a binomial distribution, and if so, what is the number of trials?

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Find the probability that a family took at least 3 vacations last year. x 0 1 2 3 4 P(x) 0.08 0.66 0.15 0.09 0.02

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

The number of typographical errors in a document follows a Poisson distribution with a mean of 2 errors per page. Let X represent the number of errors on 3 pages. Find P(Less than 3).

In a poll conducted by a survey firm, 82% of respondents said that their jobs were sometimes or always stressful. Eleven workers are chosen at random. What is the probability that more than 9 of Them find their jobs stressful?

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. What is the probability that there will be Exactly 8 bacteria in a 4-milliliter sample?