Exam 7: Discrete Probability Distributions

The distribution of the number grade one students per household in a rural community is shown below. In this distribution, the random variable x is the number grade one students per household: The standard deviation of x is ___.

On Monday mornings, customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen-minute interval. Using the Poisson distribution, the probability that five cars will arrive during the next fifteen-minute interval is ___.

The manager of a home improvement store is studying the number of on-the-job-accidents recorded. The manager provided the following probability distribution for a particular month: The mean of this distribution is ___.

The service centre of an automotive dealership expects an average of 4 complaints per day. Assume the number of complaints per day is described by a Poisson distribution, a) what is the probability of at least 2 complaints? b) how many complaints would you expect in a 2 day period?

For a discrete uniform distribution, if a = 4 and b = 5, what is standard deviation?

In a hypergeometric distribution the population, N, is finite and known.

The records of a department store show that 20% of their customers who make a purchase return the merchandise for exchange. If the distribution of the random variable x describing the number of purchases is binomial, a) what is the probability that at least 2 customers return the merchandise for exchange? b) what is the expected number and standard deviation of customers who return the merchandise for exchange?

The Human Resource manager of a corporation documents the frequency with which employees call in sick. The Human Resource manager develops the following probability distribution for the number of time staff called in sick in a particular month: Determine the expected value and the standard deviation of the probability distribution.

If x has a binomial distribution with π =.5, then the distribution of x is ___.

Circuit boards for wireless telephones are etched, in an acid bath, in batches of 100 boards. A sample of seven boards is randomly selected from each lot for inspection. A batch contains two defective boards; and x is the number of defective boards in the sample. P(x=1) is ___.

At A-Life Corporation, managers begin at $35/hour until they reach $50/hour (salaries are always to the nearest dollar). If the variable x = hourly wage has a discrete uniform distribution, what is the standard deviation of x?

The number of bags arriving on the baggage claim conveyor belt in a 3-minute time period would best be modelled with the ___.

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x=0) is ___.

If sampling is performed without replacement, the hypergeometric distribution should be used. However, the binomial may be used to approximate this if ___.

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list. She randomly selects five names from the list for validation. If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x>0) is ___.

The probability of selecting 2 baseball players and 3 basketball players for an intermural competition at a small sports camp would best be modelled with the ___.

A basketball player makes 80% of his free throws. Suppose this probability is the same for each free throw she attempts. What is probability that he makes more than 5 free throw attempts this season?

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 5 cars arriving over a five-minute interval is ___.

For the Poisson distribution the mean represents twice the value of the standard deviation.

In a binomial distribution, π, the probability of getting a successful outcome on any single trial, increases proportionately with every success.