The Poisson distribution — AS & A Level Mathematics (9709) questions by topic
Combining two independent Poisson variables for goals scored in each half of a match, testing whether a safety booklet has changed a factory's accident rate, and deciding when a binomial distribution can be approximated by a Poisson one are typical of the 31 Poisson distribution questions from 2023 to 2025, worth 3 to 14 marks.
Find, state and calculate lead the command words, with carry out and justify used where an approximation or hypothesis test must be reasoned through step by step. Because choosing the wrong parameter or approximation condition undermines an entire calculation, submit your Poisson working for instant marking, so a misapplied mean or an unjustified approximation is flagged before it carries through the rest of the question.
May–June 2025, Paper 61
It is known that 1% of houses in a certain area have a wind turbine. A random sample of 400 houses in this area is chosen for a survey on domestic heating. The number of houses in…
Answer this question and get it marked →The random variables W and X have the independent distributions Po(1.2) and Po(2.3) respectively. Find P(3 <= W + X <= 5).
Answer this question and get it marked →May–June 2025, Paper 62
The random variable X has the distribution Po(15). Write down an expression in terms of e for P(X = 12).
Answer this question and get it marked →Use suitable approximating distributions to answer the following. The random variable W has the distribution B(700, 0.005). Find P(W = 4).
Answer this question and get it marked →May–June 2025, Paper 63
At a certain shop, customers arrive independently and randomly at a constant average rate of 23.4 per hour. Find the probability that, in a randomly chosen 1-minute period, at…
Answer this question and get it marked →May–June 2025, Paper 65
The random variable X has the distribution Po(1.5). The sum of three independent values of X is denoted by S. Find P(S <= 3).
Answer this question and get it marked →The numbers of cars and trucks arriving per minute at a fuel station are modelled by independent variables with distributions Po(0.8) and Po(0.5) respectively. Find the…
Answer this question and get it marked →May–June 2024, Paper 61
A bus station has exactly four entrances. In the morning the numbers of passengers arriving at these entrances during a 10-second period have the independent distributions…
Answer this question and get it marked →Sales of cell phones at a certain shop occur singly, randomly and independently. State one further condition that must be satisfied for the number of sales in a certain time…
Answer this question and get it marked →May–June 2024, Paper 62
A random variable X has the distribution Po(145). Use a suitable approximating distribution to calculate P(X <= 150).
Answer this question and get it marked →The number of goals scored by a sports team in the first half of any match has the distribution X ~ Po(3.1). The number of goals scored by the same team in the second half of any…
Answer this question and get it marked →May–June 2024, Paper 63
The random variable X has the distribution B(4000, 0.001). Use a suitable approximating distribution to find P(2 <= X < 5).
Answer this question and get it marked →The independent random variables X and Y have the distributions Po(1.9) and Po(2.2) respectively. Find P(X + Y < 4).
Answer this question and get it marked →October–November 2024, Paper 61
The numbers of customers arriving at service desks A and B during a 10-minute period have the independent distributions Po(1.8) and Po(2.1) respectively. (a) Find the probability…
Answer this question and get it marked →The number of accidents per year on a certain road has the distribution Po(lambda). In the past the value of lambda was 3.3. Recently, a new speed limit was imposed and the…
Answer this question and get it marked →October–November 2024, Paper 62
A random variable X has the distribution B(4 500 000, 1/1 000 000). Use a Poisson distribution to calculate an estimate of P(X ≥ 4). [3]
Answer this question and get it marked →A machine puts sweets into bags at random. The numbers of lemon and orange sweets in a bag have the independent distributions Po(3.7) and Po(2.6) respectively. A bag of sweets is…
Answer this question and get it marked →October–November 2024, Paper 63
The numbers of customers arriving at service desks A and B during a 10-minute period have the independent distributions Po(1.8) and Po(2.1) respectively. Find the probability that…
Answer this question and get it marked →The number of accidents per year on a certain road has the distribution Po(lambda). In the past the value of lambda was 3.3. Recently, a new speed limit was imposed and the…
Answer this question and get it marked →May–June 2023, Paper 61
In a certain country, 20540 adults out of a population of 6012300 have a degree in medicine. Use an approximating distribution to calculate the probability that, in a random…
Answer this question and get it marked →The number of accidents per week at a certain factory has a Poisson distribution. In the past the mean has been 1.9 accidents per week. Last year, the manager gave all his…
Answer this question and get it marked →May–June 2023, Paper 62
The random variable W has a Poisson distribution. State the relationship between E(W) and Var(W).
Answer this question and get it marked →The number, X, of books received at a charity shop has a constant mean of 5.1 per day. State, in context, one condition for X to be modelled by a Poisson distribution.
Answer this question and get it marked →May–June 2023, Paper 63
It is known that 1 in 5000 people in Atalia have a certain condition. A random sample of 12 500 people from Atalia is chosen for a medical trial. The number having the condition…
Answer this question and get it marked →A new light was installed on a certain footpath. A town councillor decided to use a hypothesis test to investigate whether the number of people using the path in the evening had…
Answer this question and get it marked →October–November 2023, Paper 61
A website owner finds that, on average, his website receives 0.3 hits per minute. He believes that the number of hits per minute follows a Poisson distribution. (a) Assume that…
Answer this question and get it marked →In the past the number of enquiries per minute at a customer service desk has been modelled by a random variable with distribution Po(0.31). Following a change in the position of…
Answer this question and get it marked →October–November 2023, Paper 62
A random variable X has the distribution Po(25). Use the normal approximation to the Poisson distribution to find P(X 30). [4]
Answer this question and get it marked →A random variable X has the distribution Po(2.4). Find P(2 ≤ X < 4). [2]
Answer this question and get it marked →October–November 2023, Paper 63
A website owner finds that, on average, his website receives 0.3 hits per minute. He believes that the number of hits per minute follows a Poisson distribution. Assume that the…
Answer this question and get it marked →In the past the number of enquiries per minute at a customer service desk has been modelled by a random variable with distribution Po(0.31). Following a change in the position of…
Answer this question and get it marked →Other AS & A Level Mathematics topics
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