Exam 5: Some Important Discrete Probability Distributions

In a Poisson distribution,the mean and standard deviation are equal.

A national trend predicts that women will account for half of all business travellers in the next 3 years.To attract these women business travellers,hotels are providing more amenities that women particularly like.A recent survey of Australian hotels found that 70% offer hairdryers in the bathrooms.Consider a random and independent sample of 20 hotels. -Find the probability that more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms.

The connotation 'expected value' or 'expected gain' from playing roulette at a casino means

Instruction 5.7 A major airline keeps a record of the number of mishandled bags per 1,000 customers. In 2011, the airline had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5.7,what is the probability that in the next 1,000 customers,the airline will have at least one mishandled bag?

Instruction 5.6 The quality control manager of Marilyn's Biscuits is inspecting a batch of chocolate chip biscuits. When the production process is in control, the average number of chocolate chip parts per biscuit is 6.0. -Referring to Instruction 5.6,what is the probability that any particular biscuit being inspected has less than 5.0 or more than 8.0 chip parts?

Max wants to know how many pieces of mail he receives in 1 year.After recording the pieces of mail he receives every day for an entire year,Max calculates the total.The total number of pieces of mail he receives is a ______ variable.

Which of the following about the binomial distribution is NOT a true statement?

The number of males selected in a sample of five students taken without replacement from a class of nine females and 18 males has a hypergeometric distribution.

Instruction 5.7 A major airline keeps a record of the number of mishandled bags per 1,000 customers. In 2011, the airline had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5.7,what is the probability that in the next 1,000 customers,the airline will have less than two or more than eight mishandled bags?

The probability of receiving a 911 call on a university campus is the same every day.The probability of having received a 911 call on a single day does not change the probability of receiving a 911 call on any other day.Which of the following distributions would you use to determine the probability that a 911 call will be received next day?

Suppose that past history shows that 60% of university students prefer Brand C cola.A sample of five students is to be selected. -The probability that less than two prefer Brand C is ______.

In a game called Taxation and Evasion,a player rolls a pair of dice.If on any turn the sum is 7,11 or 12,the player gets audited.Otherwise,she avoids taxes.Suppose a player takes five turns at rolling the dice. -The probability that she gets audited no more than 2 times is ______.

What type of probability distribution will most likely be used to analyse warranty repair needs on new cars in the following problem? The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days.Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05.The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.

The expected return of the sum of two investments will be equal to the sum of the expected returns of the two investments plus twice the covariance between the investments.

Whenever p = 0.5,the binomial distribution will

Instruction 5.4 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have two such alarms in your home and they operate independently. -Referring to Instruction 5.4,the probability that neither sounds an alarm in the presence of smoke is ______

Instruction 5.3 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,if your investment preference is to maximise your expected return and not worry at all about the risk that you have to take,will you choose a portfolio that will consist of 10%,30%,50%,70% or 90% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B?

If n = 10 and p = 0.70,then the standard deviation of the binomial distribution is

Instruction 5.2 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth. X 0 1 2 3 4 5 0.1 0.2 0.4 0.1 0.0 0.0 P(X) 0 0 5 5 5 5 -Referring to Instruction 5.2,the probability of three accidents is ______.

If X has a binomial distribution with n = 5 and p = 0.1,then P(X = 2.= ______