Question

B) In a certain airport, planes landed at random times with a constant average rate of one every 10 minutes.

i. Find the probability that between two (2) and six (6) planes will landed in 10 minutes. (3 marks)​

Answer 1

0.3

Explanation:

Answer 2

The number of planes that land in a given time period follows a Poisson distribution with parameter lambda equal to the average rate of landing per unit time. In this case, lambda is equal to 0.1 planes per minute.

The probability that between 2 and 6 planes will land in 10 minutes is given by the cumulative distribution function of the Poisson distribution:

P(2 <= X <= 6) = P(X <= 6) - P(X <= 1)

Where X is the number of planes that land in 10 minutes.

Using the cumulative distribution function for the Poisson distribution, we have:

P(X <= 6) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)

P(X <= 1) = 1 - e^(-0.1 * 10) * (1 + 0.1 * 10)

Therefore,

P(2 <= X <= 6) = (1 - e^(-0.1 * 10) * (1 + 0.1 * 10 + (0.1 * 10)^2 / 2! + ... + (0.1 * 10)^6 / 6!)) - (1 - e^(-0.1 * 10) * (1 + 0.1 * 10))

The exact value of this probability can be calculated using a calculator or computer software.