Exam 6: Discrete Probability Distributions

A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. Theprobability distribution for making a particular number of hits is given below. Determine the mean for thisdiscrete probability distribution. x 0 1 2 3 4 P(x) 0.02 0.07 0.22 0.27 0.42

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

The number of goals scored at State College soccer games follows a Poisson process with a goal scoredapproximately every 18 minutes (a soccer game consists of 2 45-minute halves). What is the standarddeviation of the mean number of goals scored during a game?

Suppose the number of babies born during an eight-hour shift at a hospitalʹs maternity wing follows a Poissondistribution with a mean of 6 an hour. Find the probability that exactly four babies are born during a randomlyselected hour.3 Find the mean and standard deviation of a Poisson random variable.

Provide an appropriate response. -A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the labconducts. Prices for each weekly shipment of rats follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.25 0.3 0.45 Suppose the mean cost of the rats turned out to be $13.00 per week. Interpret this value.

A random number generator is set to generate single digits between 0 and 9. One hundred and fifty randomnumbers are generated. The probability distribution for this random number generator is given below. Whatis 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

A quiz consists of 920 true or false questions. If the student guesses on each question, what is the mean numberof correct answers?

The number of goals scored at State College soccer games follows a Poisson process with a goal scoredapproximately every 18 minutes (a soccer game consists of 2 45-minute halves). What is the mean number ofgoals scored during a game

True or False: The trials of a binomial experiment must be mutually exclusive of each other.

According to government data, the probability that an adult was never in a museum is 15%. In a randomsurvey of 10 adults, what is the probability that at least eight were in a museum?

A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. Theprobability distribution for hitting a particular number of pitches is given below. Determine the standarddeviation for this discrete probability distribution. x 0 1 2 3 4 P(x) 0.02 0.07 0.22 0.27 0.42

Among the contestants in a competition are 35 women and 20 men. If 5 winners are randomly selected, what isthe probability that they are all men?

According to government data, the probability that an adult was never in a museum is 20%. In a randomsurvey of 70 adults, what is the mean and standard deviation of the number that were never in a museum?

A local bakery has determined a probability distribution for the number of cheesecakes that they sell in a givenday. The distribution is as follows: Number sold in a day 0 5 10 15 20 Prob (Number sold) 0.07 0.1 0.22 0.23 0.38 Find the number of cheesecakes that this local bakery expects to sell in a day.

According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a randomsample of 15 households, what is the probability that the number of households with vcrs is between 10 and 12,inclusive?

An electronics store receives a shipment of 59 flat screen TVs of which 6 are defective. During the qualitycontrol inspection, 3 TVs are selected at random from the shipment for testing. The shipment will only beaccepted if all 3 TVs pass the inspection. What is the probability that the shipment will be accepted?

A manager asked her employees how many times they had given blood in the last year. The results of thesurvey 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 themean 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

A recent survey found that 69% of all adults over 50 wear sunglasses for driving. In a random sample of 20adults over 50, what is the mean and standard deviation of those that wear sunglasses?

A dictionary contains 500 pages. If there are 200 typing errors randomly distributed throughout the book, usethe Poisson distribution to determine the probability that a page contains exactly three errors.

Which of the below is not a requirement for binomial experiment?