Exam 5: Discrete Probability Distributions

It is reported that 23% of the home mortgages in Cowlitz County are "underwater".For 50 randomly selected home mortgages, compute the expected number of underwater mortgages.

Which one of the following probability distributions accurately represents the random variable "the number of times heads comes up in two tosses of a fair coin"?

Salem University's MBA program has a 55% acceptance rate.If you randomly select a sample of 20 applicants, how likely is it that no more than five of the applicants in the sample will fail to be accepted into the program?

In an ordinary 8-hour day, Roto-Drains receives calls for emergency service at an average rate of 1 per hour (otherwise, the calls appear to be random and independent).The owner currently has a crew of technicians capable of handling up to (and including) nine emergencies per day.What is the probability that on a random day there are more calls than her crew can handle?

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 exactly two stoppages in a 10-hour period.

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 20 baby boys are chosen at random.Let X represent the number of boys named Harry.What is the standard deviation of X?

The variance of a discrete random variable is a weighted average of the:

Use the Poisson probability function to find P(x < 3), where λ = 1.

A probability distribution identifies the probabilities that are assigned to all possible values of a random variable.

The step involved in building a discrete probability distribution is identifying the values for the random variable.

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.Compute the probability of no more than one request during the next hour and a half.

One of the conditions for a binomial experiment is that the trials are statistically independent.

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 no fouls in a randomly selected 2-minute interval.

Approximately 1% of all USPS package deliveries are lost.You select 10 package deliveries at random.Use the binomial probability function to compute the probability that no more than one package will be lost.

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 variance of x?

Five percent of all international video calls on Interphone.com are dropped.Suppose you randomly choose 5 recent calls.If you use the binomial function to compute the probability that exactly 3 of the 5 calls are dropped, what is the value of the binomial coefficient in you computation?

You need to buy three books for your finance course this semester.You estimate that there is 60% chance of that you can buy any one of the books cheaper online than in the bookstore.If you define "number of the finance books that will be cheaper online" as a random variable, the possible values for the random variable are, in ascending order:

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 exactly three 'shooting stars' in a randomly selected half-minute?

In recent years, 30% of the patent applications submitted to the US Patent Office have been approved.Assuming that this same rate holds in the future, if 15 new applications are submitted this year, how likely is it that at least 9 of them will be disapproved?

You plan to randomly select 10 city restaurants.Historically, 70% of city restaurants are rated "high pass" by city health inspectors.If this percentage is still true, determine the probability that among the ten restaurants you select, between 4 and 7 are rated "high pass."