Exam 5: Discrete Probability Distributions

The following table describes the results of roadworthiness tests of Ford Focus cars that are three years old (based on data from the Department of Transportation). The random variable x Represents the number of cars that failed among six that were tested for roadworthiness: ( ) 0 0.377 1 0.399 2 0.176 3 0.041 4 0.005 5 0+ 6 0+ Is the probability of getting three or more cars that fail among six cars tested significant, Determined by a cutoff value of 0.05?

Find the standard deviation, $\sigma$ , for the binomial distribution with $n = 38$ and $p = 0.4$ .

Find the standard deviation, $\sigma$ , for the binomial distribution which has $n = 48$ and $p = 3 / 5$ . Round your answer to the nearest hundredth.

The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 150 calls received By the switchboard, there are at least two wrong numbers. Round your answer to four Decimal places.

State the requirements to use the Poisson distribution as an approximation to the binomial distribution, including the mean for the Poisson distribution as an approximation to the binomial.

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

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

Use the given values of $n = 1205$ and $p = 0.98$ to find the minimum value that is not significantly low, $\mu - 2 \sigma$ , and the maximum value that is not significantly high, $\mu + 2 \sigma$ . Round your answer to the nearest hundredth unless otherwise noted.

Reader's Digest ran a sweepstakes in which prizes were listed along with chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5,000 (1 chance in 36,667,000), and $2,500 (1 chance in 27,500,000). Assuming that there is no cost of entering the sweepstakes, find the expected value of the amount won for one entry. If the cost of entering the sweepstakes is the cost of a postage stamp, is it worth entering the contest?

In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest To:

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. ( ) 0 0.1296 1 0.3456 2 0.3456 3 0.1536 4 0.0256

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing Through this tunnel, exactly two will have a flat tire. Round your answer to four decimal Places.

In a survey sponsored by Coca-Cola, subjects aged 15-65 were asked what contributes most to their happiness. The table is based on their responses. Determine whether a probability distribution is given and two reasons why or why not. Contributes Most to Happiness P(x) Family 0.77 Friends 0.15 Work/Study 0.08 Leisure 0.08 Music 0.06 Sports 0.04

In a magazine survey, 427 women are randomly selected without replacement and each woman is asked what she purchases online. Responses consist of whether clothing was identified. Determine whether the given procedure results in a distribution that is either binomial or can be treated as binomial. If not binomial, identify at least one requirement that is not satisfied.

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

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is Independent of the others.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 7 times, keeping track of the winning numbers.

The braking time of a car. Identify the given random variable as being discrete or continuous.

In one town, the number of burglaries in a week has a Poisson distribution with a mean of 1.9 burglaries. Find the probability that in a randomly selected week the number of burglaries is At least three. Use the Poisson Distribution to find the indicated probability.