Question 1

A multiple-choice test has 30 questions.There are 4 choices for each question.A student who
Has not studied for the test decides to answer all questions randomly.What type of probability
Distribution can be used to figure out his chance of getting at least 20 questions right?
A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Accepted Answer

The binomial distribution is appropriate here because each question has two possible outcomes (correct or incorrect), and the probability of getting a question right is constant across all questions.

Question 2

True or False: Another name for the mean of a probability distribution is its expected value.

Accepted Answer

The mean of a probability distribution is often referred to as its expected value, as it represents the average outcome if the experiment were repeated many times.

Question 3

True or False: The number of males selected in a sample of 5 students taken without replacement
from a class of 9 females and 18 males has a binomial distribution.

Accepted Answer

A binomial distribution requires independent trials with replacement, but selecting without replacement from a finite population does not meet these criteria.

Question 4

True or False: The Poisson distribution can be used to model a continuous random variable.

Accepted Answer

The Poisson distribution is used to model discrete random variables, specifically the number of events occurring in a fixed interval of time or space.

Question 5

The local police department must write, on average, 5 tickets a day to keep department revenues
At budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution
With a mean of 6.5 tickets per day.Interpret the value of the mean.
A) The number of tickets that is written most often is 6.5 tickets per day.
B) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.
C) If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.
D) The mean has no interpretation since 0.5 ticket can never be written.

Accepted Answer

The mean of a Poisson distribution represents the expected number of events (tickets) per time period (day), so on average, 6.5 tickets are expected to be written each day.

Question 6

True or False: The largest value that a Poisson random variable X can have is n.

Accepted Answer

A Poisson random variable can take any non-negative integer value, and there is no fixed upper limit n.

Question 7

Accepted Answer

The answer of ...

Question 8

Accepted Answer

The answer of ...

Question 9

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab
Conducts.Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per
Week.Interpret this value.
A) Most of the weeks resulted in rat costs of $13.00.
B) The median cost for the distribution of rat costs is $13.00.
C) The expected or mean cost for all weekly rat purchases is $13.00.
D) The rat cost that occurs more often than any other is $13.00.

Accepted Answer

The mean cost of $13.00 per week indicates that the average cost of rats per week over the year is $13.00.

Question 10

A financial analyst is presented with information on the past records of 60 start-up companies
And told that in fact only 3 of them have managed to become highly successful.He selected 3
Companies from this group as the candidates for success.To analyze his ability to spot the
Companies that will eventually become highly successful, he will use what type of probability
Distribution?
A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Accepted Answer

The hypergeometric distribution is used when sampling without replacement from a finite population, which is the case here as the analyst selects 3 companies from a group of 60.

Question 11

True or False: The number of customers arriving at a department store in a 5-minute period has a
binomial distribution.

Accepted Answer

A binomial distribution is used for a fixed number of independent trials with two possible outcomes. The number of customers arriving is better modeled by a Poisson distribution, which is used for counting the number of events in a fixed interval of time or space.

Question 12

True or False: The number of customers arriving at a department store in a 5-minute period has a
Poisson distribution.

Accepted Answer

The Poisson distribution is often used to model the number of events occurring within a fixed interval of time or space, such as the number of customers arriving at a store in a given time period.

Question 13

True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson
process.The mean number of airplanes arriving per minute is 3.The probability that exactly 6
planes arrive in the next minute is 0.05041.

Accepted Answer

The probability of exactly k events in a Poisson distribution is given by $ P(k; \lambda) = \frac{e^{-\lambda} \lambda^k}{k!} $. For k=6 and λ=3, this calculates to approximately 0.05041.

Question 14

True or False: In a Poisson distribution, the mean and standard deviation are equal.

Accepted Answer

In a Poisson distribution, the mean is equal to the variance, not the standard deviation. The standard deviation is the square root of the mean.

Question 15

True or False: The number of males selected in a sample of 5 students taken without replacement
from a class of 9 females and 18 males has a hypergeometric distribution.

Accepted Answer

The hypergeometric distribution models the number of successes in a sample drawn without replacement from a finite population, which fits the scenario of selecting males from a class of males and females.

Question 16

True or False: Suppose that a judge's decisions follow a binomial distribution and that his verdict
is incorrect 10% of the time.In his next 10 decisions, the probability that he makes fewer than 2
incorrect verdicts is 0.736.

Accepted Answer

The probability of making fewer than 2 incorrect verdicts (0 or 1 incorrect) can be calculated using the binomial distribution formula. For 0 incorrect verdicts: P(X=0) = (10 choose 0) * (0.1)^0 * (0.9)^10 = 0.3487. For 1 incorrect verdict: P(X=1) = (10 choose 1) * (0.1)^1 * (0.9)^9 = 0.3874. Adding these probabilities gives 0.3487 + 0.3874 = 0.7361, which rounds to 0.736.

Question 17

Accepted Answer

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Question 18

True or False: The diameters of 10 randomly selected bolts have a binomial distribution.

Accepted Answer

The diameters of bolts are continuous measurements, which are typically modeled by a normal distribution, not a binomial distribution. The binomial distribution is used for discrete outcomes, such as the number of successes in a series of trials.

Question 19

On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery
Store.What type of probability distribution can be used to find out the probability that there will
Be no customer arriving at a checkout counter?
A) binomial distribution.
B) Poisson distribution.
C) hypergeometric distribution.
D) none of the above.

Accepted Answer

The Poisson distribution is used for modeling the number of events (such as customer arrivals) in a fixed interval of time or space when these events occur with a known constant mean rate and independently of the time since the last event.

Question 20

True or False: In a Poisson distribution, the mean and variance are equal.

Accepted Answer

In a Poisson distribution, the mean (λ) is equal to the variance, which is a defining property of this distribution.

Quiz 5: Discrete Probability Distributions

A multiple-choice test has 30 questions.There are 4 choices for each question.A student who Has not studied for the test decides to answer all questions randomly.What type of probability Distribution can be used to figure out his chance of getting at least 20 questions right?

True or False: Another name for the mean of a probability distribution is its expected value.

True or False: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution.

True or False: The Poisson distribution can be used to model a continuous random variable.

The local police department must write, on average, 5 tickets a day to keep department revenues At budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution With a mean of 6.5 tickets per day.Interpret the value of the mean.

True or False: The largest value that a Poisson random variable X can have is n.

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab Conducts.Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per Week.Interpret this value.

True or False: The number of customers arriving at a department store in a 5-minute period has a binomial distribution.

True or False: The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.

True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson process.The mean number of airplanes arriving per minute is 3.The probability that exactly 6 planes arrive in the next minute is 0.05041.

True or False: In a Poisson distribution, the mean and standard deviation are equal.

True or False: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a hypergeometric distribution.

True or False: Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% of the time.In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

True or False: The diameters of 10 randomly selected bolts have a binomial distribution.

On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery Store.What type of probability distribution can be used to find out the probability that there will Be no customer arriving at a checkout counter?

True or False: In a Poisson distribution, the mean and variance are equal.