Exam 5: Discrete Probability Distributions

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.

Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

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?

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

Identify the given random variable as being discrete or continuous. The cost of a randomly selected orange.

Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn't possible. He said that the expected value was the most likely value in a single roll of the die, and since it wasn't possible for a die to turn up with a value of 3.5, the expected value couldn't possibly be 3.5. Who is right?

Suppose that weight of adolescents is being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected Adolescents, where x is the number who are considered morbidly obese. Is it significant to Have no obese subjects among three randomly selected adolescents? 0 0.111 1 0.215 2 0.450 3 0.224

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

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.

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 significant to get 634 consumers who recognize the Dull Computer Company name? Consider as significant any result that differs from the mean by more than 2 standard deviations. That is, significant values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$

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.

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

List the three methods for finding binomial probabilities in the table below, and then complete the table to discuss the advantages and disadvantages of each. Methods Advantage Disadvantage

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

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.

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.

Based on a Comcast survey, there is a 0.8 probability that a randomly selected adult will watch prime-time TV live, instead of online, on DVR, etc. Assume that seven adults are Randomly selected. Find the probability that fewer than three of the selected adults watch Prime-time live.

A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch.