Exam 5: Probability Distributions

Provide an appropriate response. -Previously we learned to find the three important characteristics of data: the measure of central tendency, the measure of variation, and the nature of the distribution, We can find the same three characteristics for a binomial distribution. Given a binomial distribution with p = 0.4 and n = 8, find the three characteristics.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. - () 0 0.287 1 0.225 2 -0.027 3 0.339 4 0.080 5 0.096

Solve the problem. -A company manufactures batteries in batches of 28 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch.

Use the normal distribution to approximate the desired probability. -Find the probability of selecting exactly 5 girls.

Solve the problem. -A contractor is considering a sale that promises a profit of $23,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such)of $13,000 with a probability of 0.3. What is the expected profit?

Identify the given random variable -The number of phone calls between New York and California on Thanksgiving day

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $n = 64 , x = 3 , p = 0.04$

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 $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$ . -A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 481 consumers who recognize the Dull Computer Company name?

Solve the problem. -A company manufactures batteries in batches of 29 and there is a 3% rate of defects. Find the mean number of defects per batch.

Provide an appropriate response. -A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run, the player can expect to win 0. Consider the following game. The game costs $1 to play and the winnings are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following probabilities apply. What are your expected winnings? Does the game favor the player or the owner? Outcome Probability Red .02 Blue .04 Yellow .16 White .78

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. - $n = 10 , x = 2 , p = 0.5$

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 $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$ . -The Acme Candy Company claims that 8% of the jawbreakers it produces actually result in a broken jaw. Suppose 9571 persons are selected at random from those who have eaten a jawbreaker produced at Acme Candy Company. Would it be unusual for this sample of 9571 to contain 792 persons with broken jaws?

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. -n = 1507; p = .57

Answer the question. -Rolling a single die 19 times, keeping track of the numbers that are rolled.

Answer the question. -Suppose that a law enforcement group studying traffic violations determines that the accompanying table describes the probability distribution for five randomly selected people, where x is the number that have received a speeding ticket in the last 2 years. Is it unusual to find no speeders among five randomly selected people? x P(x) 0 0.08 1 0.18 2 0.25 3 0.22 4 0.19 5 0.08

A car insurance company has determined that 7% of all drivers were involved in a car accident last year. Among the 11 drivers living on one particular street, 3 were involved in a car accident last year. If 11 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?

Ten apples, four of which are rotten, are in a refrigerator. Three apples are randomly selected without replacement. Let the random variable x represent the number chosen that are rotten. Construct a table describing the probability distribution, then find the mean and standard deviation for the random variable x.

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? -n = 189, p = 0.13