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Exam 5: Discrete Probability Distributions

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Question 51

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Requests for a chat with a customer service representative on MaxTrend.com's website conform roughly to the Poisson conditions.The average number of requests is six per hour.The probability is approximately 6% that fewer than what number of requests will be made in the next hour.

A) 5
B) 2
C) 9
D) 4
E) 3

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Question 52

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Use the Poisson probability function to find P(x = 3) , where λ= 7.

A) .6072
B) .7113
C) .5021
D) .4329
E) .4789

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Question 53

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Suppose a random variable X describes the outcome of a binomial experiment with 30 trials and a 0.80 probably of success for each trial.The shape of the distribution of X is:

The average number of wind turbines at the vast Kindler Range Wind Farm that malfunction and need repair is 2.3 per day.Assume that all the Poisson conditions are met.Letting x represent values of the random variable "number of turbines that malfunction during any one day," what is the expected value of x?

Use the Poisson distribution to approximate the binomial probability P(x < 2) when n = 800, p = .002 .

The first step in producing a probability distribution is to identify values for the random variable.

Below is a table showing the probability distribution for the random variable x.Compute the standard deviation of the random variable.

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.Use the binomial function to compute the probability that none of the calls are dropped.

During a meteor shower, 'shooting stars' occur at an average rate of 12 per minute or .2 per second.Assume all the Poisson conditions are met.What is the probability of no more than two 'shooting stars' in a particular second?

The binomial probability for P(x = 5) , where n = 20, p =.1 is .0319.If you use the Poisson distribution to approximate this binomial probability, what probability would you produce?

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.Use the binomial function to compute the probability that no more than two calls are dropped.

For a binomial distribution, find P(3 < x < 5) , where n = 15, p = .5.

At work, Serge receives an average of four e-mails every hour.Assuming that all of the Poisson conditions are met, use the Poisson probability function to calculate the probability that Serge receives no e-mails in the next 15 minutes.

The most popular names for babies born in the United Kingdom in 2012 were Harry and Amelia.Of the roughly 400,000 baby boys born in the UK in 2012, two percent were named Harry, while two percent of the girls born that year were named Amelia (Source: UK Office for National Statistics, Baby Names, England and Wales, 2012) .Suppose that 30 baby girls are chosen at random.Let X represent the number of girls named Amelia.What is the expected value of X?

The standard deviation of a discrete probability distribution is the positive square root of the variance, which determines the expected value of the distribution.

Which of the following is NOT one of the steps involved in building a discrete probability distribution?

Which of the following is a condition for a binomial probability experiment?

On average stoppages on the assembly line at Jamari Industries have a Poisson distribution with a mean of .1 per hour.Use the Poisson probability function to determine the probability of having no stoppages in a 20 hour period.

Below is a table showing the probability distribution for the random variable x.Compute the variance of the random variable.

In a study of NBA basketball games, it was reported that there are, on average, .3 fouls committed per minute.Assume all the Poisson conditions are met.Determine the probability of exactly one foul in a randomly selected minute.