Exam 6: Discrete Probability Distributions

Determine Whether a Probability Experiment is a Binomial Experiment -Decide whether the experiment is a binomial experiment. If it is not, explain why. You test four flu medicines. The random variable represents the flue medicine that is most effective.

Compute the Variance and Standard Deviation of a Discrete Random Variable -A manager at a local company asked his 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 P(x) represents the probability of selecting an employee who had given blood that percent of the time. What is the standard deviation for the 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

Interpret the Mean of a Discrete Random Variable as an Expected Value -A legendary football coach was known for his winning seasons. He consistently won nine or more games per season. Suppose $x$ equals the number of games won up to the halfway mark (six games) in a 12-game season. If this coach and his team had a probability $p = 0.8$ of winning any one game (and the winning or losing of one game was independent of another), then the probability distribution of the number $x$ of winning games in a series of six games is: x P(x) 0 0.000064 1 0.001536 2 0.015360 3 0.081920 4 0.245760 5 0.393216 6 0.262144 Find the expected number of winning games in the first half of the season for this coach's football teams.

Classify the following random variable according to whether it is discrete or continuous -the number of pills in an aspirin bottle

Construct Probability Histograms -Calculate the mean for the discrete probability distribution shown here.

Determine Whether a Probability Experiment is a Binomial Experiment -Decide whether the experiment is a binomial experiment. If it is not, explain why. Each week, a gambler plays blackjack at the local casino. The random variable is the number of times per week the player wins.

Construct Probability Histograms -A random number generator is set to generate single digits between 0 and 9 . One hundred and fifty random numbers are generated. The probability distribution for this random number generator is given below. What is the mean of this distribution? x 0 1 2 3 4 5 6 7 8 9 P(x) 0.09 0.12 0.11 0.08 0.09 0.13 0.10 0.07 0.10 0.11

Compute the Mean and Standard Deviation of a Binomial Random Variable -A quiz consists of 930 true or false questions. If the student guesses on each question, what is the standard deviation of the number of correct answers

Interpret the Mean of a Discrete Random Variable as an Expected Value -An automobile insurance company estimates the following loss probabilities for the next year on a $\$ 25,000$ sports car: Total loss: 0.001 50\% loss: 0.01 25\% loss: 0.05 10\% loss: 0.10 Assuming the company will sell only a $\$ 500$ deductible policy for this model (i.e., the owner covers the first $\$ 500$ damage), how much annual premium should the company charge in order to average $\$ 450$ profit per policy sold?

Classify the following random variable according to whether it is discrete or continuous -the cost of a road atlas

Compute Probabilities of Binomial Experiments -A quiz consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the quiz a student must get 60% or better on the quiz. If a student randomly guesses, what is the probability that the student will pass the quiz

Compute Probabilities of Binomial Experiments -The probability that a football game will go into overtime is 13%. What is the probability that two of three football games will go to into overtime

Construct Probability Histograms -The random variable $\mathrm { x }$ represents the number of tests that a pet entering an animal shelter will have along with the corresponding probabilities. Graph the probability histogram. x P(x) 0 1 2 3 4

Compute Probabilities of Binomial Experiments -According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that the number of households with vcrs is between 10 and 12, inclusive

Classify the following random variable according to whether it is discrete or continuous -the speed of a car on a New York tollway during rush hour traffic

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 mean number of goals scored during a game

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 two or fewer were never in a museum

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 5 10 15 20 P(x) 0.10 -0.30 0.50 0.70

Compute Probabilities of a Poisson Random Variable -A local animal rescue organization receives an average of 0.55 rescue calls per hour. Use the Poisson distribution to find the probability that during a randomly selected hour, the organization will receive fewer than two calls.

Compute Probabilities of Binomial Experiments -Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three girls in ten births.