Exam 5: Discrete Probability Distributions

The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Based on this distribution,the expected number of accidents in a given day is:

If a binomial distribution applies with a sample size of n = 20,find the probability of 5 successes if the probability of a success is 0.40.

Given a binomial distribution with n = 8 and p = 0.40,obtain the mean.

The manager of a movie theater has determined that the distribution of customers arriving at the concession stand is Poisson distributed with a standard deviation equal to 2 people per 10 minutes.What is the probability that 0 customers arrive during a 10-minute period?

The U.S.Census Bureau (Annual Social & Economic Supplement)collects demographics concerning the number of people in families per household.Assume the distribution of the number of people per household is shown in the following table: Compute the variance and standard deviation of the number of people in families per household.

Beacon Hill Trees & Shrubs currently has an inventory of 10 fruit trees,8 pine trees,and 14 maple trees.It plans to give 4 trees away at next Saturday's lawn and garden show in the city park.The 4 winners can select which type of tree they want.Assume they select randomly. What is the probability that no fruit trees and 2 of each of the others will be selected?

Jennings Assembly in Hartford,Connecticut,uses a component supplied by a company in Brazil.The component is expensive to carry in inventory and consequently is not always available in stock when requested.Furthermore,shipping schedules are such that the lead time for transportation of the component is not a constant.Using historical records,the manufacturing firm has developed the following probability distribution for the product's lead time.The distribution is shown here,where the random variable is the number of days between the placement of the replenishment order and the receipt of the item. What is the average lead time for the component?

When dealing with the number of occurrences of an event over a specified interval of time or space,the appropriate probability distribution is hypergeometric.

The probability that a product is found to be defective is 0.10.If we examine 50 products,which of the following has the highest probability?

The roll of a pair of dice has the following probability distribution,where the random variable is the sum of the values produced by each die: Calculate the expected value of x.

Arrivals to a bank automated teller machine (ATM)are distributed according to a Poisson distribution with a mean equal to three per 15 minutes.Determine the probability that in a given 15-minute segment no customers will arrive at the ATM.

A small city has 2 ambulances.Emergency calls for ambulances arrive randomly with an average of 0.2 calls per hour.They are concerned about the possibility of both ambulances being busy when an additional call comes in.What is the probability of more than 2 calls in a 1-hour period? Determine the correct distribution,explain why it is the best distribution to use,and find the probability.

Six managers at a company all enjoy golf.Each Saturday,four of the six get together for 18 holes of golf.They have decided to set up a schedule so that the same foursome does not play twice before all possible foursomes have played.The number of weekends that will pass before the same group would play twice is 15.

What is the difference between a discrete random variable and a continuous random variable?

Cramer's Bar and Grille in Dallas can seat 130 people at a time.The manager has been gathering data on the number of minutes a party of four spends in the restaurant from the moment they are seated to when they pay the check. What is the mean number of minutes for a dinner party of four?

Beacon Hill Trees & Shrubs currently has an inventory of 10 fruit trees,8 pine trees,and 14 maple trees.It plans to give 4 trees away at next Saturday's lawn and garden show in the city park.The 4 winners can select which type of tree they want.Assume they select randomly. What is the probability that all 4 winners will select the same type of tree?

Under what conditions is the binomial distribution symmetric?

If a distribution is considered to be Poisson with a mean equal to 11,the most frequently occurring value for the random variable will be:

A mid-management team consists of 10 people,6 males and 4 females.Recently top management selected 4 people from this team for promotion.It was stated that the selections were based on random selection.All 4 people selected were males.The females are upset and believe that there may have been more than random selection involved here.What probability distribution should be used to analyze this situation and what is the probability that all 4 promotions would go to males if the selections were random? Do you believe that the females have a valid complaint in this situation?

A local paint store carries 4 brands of paint (W,X,Y,and Z).The store has 5 cans of W,3 cans of X,6 cans of Y,and 15 cans of Z,all in white.It is thought that customers have no preference for one of these brands over another.If this is the case,what is the probability that the next 5 customers will select 1 can of W,X,Y and 2 cans of brand Z?