SB1-SB2 Modelling with the Poisson distribution Quiz: AQA Further Maths, Unit 4

The 20 questions

1. Which of the following is NOT a standard condition for a Poisson model to be suitable?

   • Events occur independently of each other
   • Events occur singly, not in pairs
   • Events occur at fixed, predetermined times
   • Events occur at a constant average rate

2. What does the notation X ~ Po(lambda) mean?

   • X is a continuous uniform variable on lambda
   • X follows a Poisson distribution with mean lambda
   • X is a normal variable with variance lambda
   • X follows a binomial distribution with lambda trials

3. For X ~ Po(lambda), which expression gives P(X = x)?

   • e^(-lambda) x^lambda / lambda!
   • e^(-lambda) lambda^x / x!
   • e^(lambda) lambda^x / x!
   • lambda^x / x!

4. In a Poisson model, what does the parameter lambda represent?

   • The standard deviation of the number of events
   • The largest possible number of events
   • The mean number of events in the interval
   • The probability of no events

5. For X ~ Po(lambda), what is P(X = 0)?

   • lambda e^(-lambda)
   • e^(-lambda)
   • e^(lambda)
   • 1 - e^(-lambda)

6. Which of these is most suitable to be modelled by a Poisson distribution?

   • Rainfall amounts in millimetres
   • Customer arrivals per hour at a shop
   • Heights of students in a class
   • Marks out of 100 in a test

7. What values can a Poisson random variable take?

   • Only positive numbers with decimals
   • Any real number
   • Only values between 0 and 1
   • The non-negative integers 0, 1, 2, ...

8. Calls to a helpline occur at an average rate of 4 per minute. What is the probability of exactly one call in a minute, to 4 decimal places?

   • 0.2381
   • 0.0183
   • 0.0733
   • 0.1465

9. X ~ Po(3). What is P(X = 0) to 4 decimal places?

   • 0.0067
   • 0.2240
   • 0.1494
   • 0.0498

10. X ~ Po(3). What is P(X = 2) to 4 decimal places?

    • 0.1494
    • 0.0498
    • 0.4482
    • 0.2240

11. X ~ Po(2). What is P(X >= 1) to 4 decimal places?

    • 0.1353
    • 0.2707
    • 0.5940
    • 0.8647

12. X ~ Po(2). What is P(X = 3) to 4 decimal places?

    • 0.2707
    • 0.1804
    • 0.1353
    • 0.0902

13. Traffic passes a point at an average rate of 0.5 vehicles per minute. Using a Poisson model, what is the probability of no vehicles in one minute, to 4 decimal places?

    • 0.5000
    • 0.3679
    • 0.6065
    • 0.1353

14. X ~ Po(1). What is P(X <= 2) to 4 decimal places?

    • 0.3679
    • 0.9197
    • 0.7358
    • 0.5000

15. X ~ Po(5). What is P(X = 5) to 4 decimal places?

    • 0.1755
    • 0.0067
    • 0.1404
    • 0.2000

16. For X ~ Po(lambda), P(X = 0) = 0.2. What is lambda, to 2 decimal places?

    • 0.22
    • 5.00
    • 0.80
    • 1.61

17. For X ~ Po(lambda), for what value of lambda are P(X = 1) and P(X = 2) equal?

    • 2
    • 1/2
    • 4
    • 1

18. X ~ Po(3). What is P(X >= 2) to 4 decimal places?

    • 0.1991
    • 0.1494
    • 0.8009
    • 0.5768

19. Customers arrive at a rate of 3 per hour, modelled as Po(6) over two hours. What is P(X >= 2) to 4 decimal places?

    • 0.0174
    • 0.0500
    • 0.9500
    • 0.9826

20. For X ~ Po(lambda), P(X = 1) = 3 P(X = 0). What is lambda?

    • 9
    • 0.5
    • 3
    • 1/3

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