Exam 5: Discrete Probability Distributions

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma \text { and the maximum usual value } \mu + 2 \sigma$ . Round your answer to the nearest hundredth unless otherwise noted. - $\mathrm { n } = 1070 , \mathrm { p } = 0.88$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Choosing 10 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the number of red marbles chosen.

Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 1617 ; \mathrm { p } = 0.57$

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x( girls ) P(x) x (girls) P(x) x( girls ) P(x) 0 0.000 5 0.122 10 0.061 1 0.001 6 0.183 11 0.022 2 0.006 7 0.209 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 -Find the probability of selecting 2 or more girls.

Identify the given random variable as being discrete or continuous. -The number of field goals kicked in a football game

Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected value?

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. - $n = 30 , x = 5 , p = \frac { 1 } { 5 }$

Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45 probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05 probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

Find the indicated probability. Round to three decimal places. -A car insurance company has determined that 8% of all drivers were involved in a car accident last year. Among the 14 drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?

List the two requirements for a probability histogram. Discuss the relationship between the sum of the probabilities in a probability distribution and the total area represented by the bars in a probability histogram.

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than µ - 2? or greater than µ + 2?. -The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 423 jawbreakers that weigh more than .4 ounces?

Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. -In a certain town, 50% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. () 0 0.0625 1 0.2500 2 0.3750 3 0.2500 4 0.0625

Identify the given random variable as being discrete or continuous. -The number of oil spills occurring off the Alaskan coast

A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.50, 0.38, 0.10, and 0.02, respectively. Find the standard deviation for the probability distribution. Round answer to the nearest hundredth.

Find the indicated probability. Round to three decimal places. -In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

The brand name of a certain chain of coffee shops has a 50% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is Interested in opening a coffee shop in the town. He selects a random sample of 9 Coffleton Residents. Find the probability that the number that recognize the brand name is not 4.

Find the indicated probability. Round to three decimal places. -An airline estimates that 91% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the Number of people who show up will exceed the capacity of the plane?

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than µ - 2? or greater than µ + 2?. -According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be Unusual to find that 900 of the 2500 televisions are tuned to "Eyewitness News"?

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2?. Round your answer to the nearest hundredth unless otherwise noted. - $\mathrm { n } = 2428 , \mathrm { p } = 0.577 \text { Round your answers to the nearest thousandth. }$