Exam 6: Discrete Probability Distributions

Compute Probabilities of Binomial Experiments -According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that at least eight were in a museum

Compute Probabilities of Binomial Experiments -Fifty percent of the people that use the Internet order something online. Find the probability that only four of 8 Internet users will order something online.

Compute Probabilities of a Poisson Random Variable -The number of goals scored at State College soccer games follows a Poisson process with a goal scored approximately every 18 minutes (a soccer game consists of 2 45-minute halves). What is the standard deviation of the mean number of goals scored during a game

Compute Probabilities of a Poisson Random Variable -Suppose the number of babies born during an 8-hour shift at a hospital s maternity wing follows a Poisson distribution with a mean of 7 an hour. Some people believe that the presence of a full moon increases the number of births that take place. Suppose during the presence of a full moon, County Hospital experienced eight consecutive hours with more than eight births. Based on this fact, comment on the belief that the full moon increases the number of births.

Identify Discrete Probability Distributions -Consider the discrete probability distribution to the right when answering the following question. Find the probability that $x$ equals 4 . x 2 4 7 9 P(x) 0.05 ? 0.13 0.14

Identify Discrete Probability Distributions -Given the table of probabilities for the random variable $x$ , does this form a probability distribution? Answer Yes or No. x 0 1 2 3 4 P(x) 0.02 0.07 0.22 0.27 0.42

Construct Probability Histograms -The random variable $x$ represents the number of credit cards that students have along with the corresponding probabilities. Graph the probability histogram. () 0 0.49 1 0.05 2 0.32 3 0.07 4 0.07

Compute Probabilities of a Poisson Random Variable -The number of traffic accidents that occurs on a particular stretch of road during a month follows a Poisson distribution with a mean of 7.2. Find the probability that less than two accidents will occur on this stretch of road during a randomly selected month.

Compute the Mean and Standard Deviation of a Binomial Random Variable -The probability that an individual has 20-20 vision is 0.17. In a class of 80 students, what is the mean and standard deviation of the number with 20-20 vision in the class

Compute Probabilities of Binomial Experiments -The probability that an individual has 20-20 vision is 0.15. In a class of 32 students, what is the probability of finding five people with 20-20 vision

Classify the following random variable according to whether it is discrete or continuous -the pressure of water coming out of a fire hose

Compute the Mean and Standard Deviation of a Binomial Random Variable -A quiz consists of 20 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers.

Determine Whether a Probability Experiment is a Binomial Experiment -The trials of a binomial experiment must be mutually exclusive of each other.

Classify the following random variable according to whether it is discrete or continuous -the number of goals scored in a hockey game

Compute Probabilities of Binomial Experiments -We believe that 87% of the population of all Calculus I students consider calculus an exciting subject. Suppose we randomly and independently selected 25 students from the population. If the true percentage is really 87%, find the probability of observing 24 or more of the students who consider calculus to be an exciting subject in our sample of 25.

Compute Probabilities of a Poisson Random Variable -Suppose x is a random variable for which a Poisson probability distribution with = 11.4 provides a good characterization. Find for x.

Compute the Variance and Standard Deviation of a Discrete Random Variable -The random variable $x$ represents the number of tests that a patient entering a clinic will have along with the corresponding probabilities. Find the mean and standard deviation for the random variable $x$ . () 0 1 2 3 4

Compute the Mean and Standard Deviation of a Hypergeometric Random Variable -In a lottery, a player must choose 6 numbers between 1 and 36 inclusive. Six balls are then randomly selected from an urn containing 36 balls numbered from 1 to 36 . The random variable $X$ represents the number of matching numbers. What are the mean and standard deviation of the random variable $X$ ?

Compute the Mean and Standard Deviation of a Binomial Random Variable -A quiz consists of 190 true or false questions. If the student guesses on each question, what is the mean number of correct answers

Construct Probability Histograms -A manager asked her employees how many times they had given blood in the last year. The results of the survey are given below. The random variable $x$ represents the number of times a person gave blood and $\mathrm { P } ( \mathrm { x } )$ represents the probability of selecting an employee who had given blood that percent of the time. What is the mean number of times a person gave blood based on this survey? x 0 1 2 3 4 5 6 P(x) 0.30 0.25 0.20 0.12 0.07 0.04 0.02