Question 1

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10 calls a day.The probability of 2 or more 000 calls in a day is ______

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Question 2

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10.0 calls a day.The standard deviation of the number of 000 calls in a day is ______

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Question 3

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be between 1 and 3 inclusive power outages in a year is ______

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Question 4

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be no more than 1 power outage in a year is______

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Question 5

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 4.0 chip parts?

Accepted Answer

The answer of Instruction 5.6
The quality control manager of Marilyn's...

Question 6

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be at least 3 power outages in a year is ______.

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Question 7

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?
A) Binomial distribution.
B) Poisson distribution.
C) Hypergeometric distribution.
D) None of the above.

Accepted Answer

Since the probability of receiving a 911 call remains constant, the situation can be modeled using the Poisson distribution. The Poisson distribution is used to model the number of events or occurrences in a fixed interval of time or space, assuming that the events occur randomly and independently, and with a constant rate. Therefore, it is the best choice to determine the probability of receiving a 911 call next day. The binomial distribution is used when there are a fixed number of trials or experiments, with two possible outcomes (success/failure), and independent events. The hypergeometric distribution is used when sampling without replacement from a finite population, where the events are not independent. Neither of these applies to the given scenario.

Question 8

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be at least 1 power outage in a year is ______.

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Question 9

It was believed that the probability of a small business that declared bankruptcy per month was the same in any month.Also the number of small businesses that declared bankruptcy was the same every month.Which of the following distributions would you use to determine the probability that more than three bankruptcies will occur next month?
A) Binomial distribution.
B) Poisson distribution.
C) Hypergeometric distribution.
D) None of the above.

Accepted Answer

The scenario described is a classic example of the Poisson distribution, which models the number of occurrences of a rare event in a specified interval of time or space. The Poisson distribution assumes that the events are independent, occur at a constant rate, and have a low probability of occurring in any given interval. In this case, the bankruptcy of small businesses is a rare event, occurs independently of each other, and has a constant probability per month. Hence, the Poisson distribution is the most appropriate model to use for calculating the probability of more than three bankruptcies occurring next month. The binomial distribution assumes a fixed number of trials with a binary outcome, which is not applicable here. The hypergeometric distribution models the probability of drawing a specific combination of items from a finite population without replacement, which is also not relevant to this scenario.

Question 10

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10 calls a day.The probability of seven 000 calls in a day is ______

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Question 11

The local police department must write,on average,five 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 6.4 tickets per day.
-Find the probability that exactly six tickets are written on a randomly selected day from this population.

Accepted Answer

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Question 12

The local police department must write,on average,five 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 6.4 tickets per day.
-Find the probability that less than six tickets are written on a randomly selected day from this population.

Accepted Answer

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Question 13

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be exactly 3 power outages in a year is______.

Accepted Answer

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Question 14

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 fewer than 5.0 chip parts?

Accepted Answer

The answer of Instruction 5.6
The quality control manager of Marilyn's...

Question 15

Suppose the probability of a power outage at a nuclear power plant on a single day is the same every day of the year.Also the probability of having a power outage on a single day does not increase or decrease the probability of a power outage on another day.Which of the following distributions would you use to determine the probability that a power outage will occur next Monday?
A) Binomial distribution.
B) Poisson distribution.
C) Hypergeometric distribution.
D) None of the above.

Accepted Answer

The Poisson distribution is appropriate when the probability of success is the same for each interval or unit of time, and events occur independently of each other. In this case, the probability of a power outage is the same every day, and events occurring on one day do not affect the probability of an outage on another day. Therefore, the Poisson distribution is the best choice to determine the probability of a power outage on a single day, including next Monday. The binomial distribution assumes a fixed number of trials or attempts, which does not apply in this scenario, and the hypergeometric distribution assumes sampling without replacement, which does not apply here either.

Question 16

Suppose that past history shows that 6% of college students prefer Brand A cola.A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Brand A cola?
A) Normal distribution.
B) Hypergeometric distribution.
C) Poisson distribution.
D) None of the above.

Accepted Answer

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Question 17

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.
-Find the probability that more than three bankruptcies occur next month.

Accepted Answer

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Question 18

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The variance of the number of power outages is______

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Question 19

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.
-Find the probability that exactly five bankruptcies occur next month.

Accepted Answer

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Question 20

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10 calls a day.The probability of seven or eight 000 calls in a day is ______

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Quiz 5: Some Important Discrete Probability Distributions

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10 calls a day.The probability of 2 or more 000 calls in a day is ______

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10.0 calls a day.The standard deviation of the number of 000 calls in a day is ______

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be between 1 and 3 inclusive power outages in a year is ______

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be no more than 1 power outage in a year is______

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be at least 3 power outages in a year is ______.

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be at least 1 power outage in a year is ______.

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10 calls a day.The probability of seven 000 calls in a day is ______

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be exactly 3 power outages in a year is______.

Suppose that past history shows that 6% of college students prefer Brand A cola.A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Brand A cola?

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. -Find the probability that more than three bankruptcies occur next month.

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The variance of the number of power outages is______

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. -Find the probability that exactly five bankruptcies occur next month.

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10 calls a day.The probability of seven or eight 000 calls in a day is ______