Question

On average, Nancy has noticed that 18 trucks pass by her apartment daily (24 hours). In order to find the probability that more than 2 trucks will pass her apartment in a 2-hour time period using the Poisson distribution, find the average number of trucks per 2 hours. Round your answer to three decimal places, if necessary.

Answer 1

18 trucks pass by her apartment daily (24 hours)

average number of trucks per 2 hours = 18/24*2 = 1.5 trucks

poisson probability distribution

P(X=x) = e-λλx/x!

here, λ = 1.5

P(more than 2) = P(X>2) = 1 - P(X=0) - P(X=1) - P(X=2) = 1-0.2231 - 0.3347 - 0.2510 = 0.1912

Answer 2

Given:

• Average trucks in 24 hours (λ) = 18.

1. Calculate the rate per hour:

   $$\text{Rate per hour}=\frac{18\text{ trucks}}{24\text{ hours}}=0.75\text{ trucks/hour}$$

2. Find the rate for 2 hours:

   $$\text{Average for 2 hours}=0.75\times 2=1.5\text{ trucks}$$

This value (1.5) is the λ (lambda) for the Poisson distribution when calculating probabilities for a 2-hour window.

Answer : The average number of trucks per 2-hour period is 1.5.