19.X.6. Solved Examples

Try these first

1. 1.

   If the average number of cars passing an intersection is 10 per hour, what is the probability of exactly 5 cars arriving in the next hour?

   Hint

   Use the Poisson formula with λ = 10.

2. 2.

   How would you express the probability of no events occurring when λ = 3?

   Hint

   Remember the factorial of zero is 1.

3. 3.

   What is the mean of a Poisson distribution?

   • a) e
   • b) λ
   • c) Standard deviation

   Hint

   Recall the properties of Poisson distribution.

4. 4.

   True or False: The variance of the Poisson distribution is equal to its mean.

   • True
   • False

   Hint

   Think about the formula relating mean and variance.

5. 5.

   A library gains, on average, 2 new books every week. What is the probability that it will gain exactly 5 new books next week?

   Hint

   Apply the Poisson formula providing your λ and k.

6. 6.

   During a busy season, a restaurant receives about 10 customers every hour. Calculate the probability that between 8 to 12 customers arrive during the next hour.

   Hint

   Start with individual probabilities and use the Poisson formula for each case.