Question

the poisson distribution

1. the flaws in a piece of timber occur at the rate of 0.08 per linear foot. the random variable x is the number of flaws in the next 20 linear feet timber. state the values of λ and t.

Explanation:

Step1: Recall Poisson distribution formula parameters

In Poisson distribution for events over an interval, \(\lambda\) is the average rate of occurrence per unit interval and \(t\) is the number of units in the interval.

Step2: Identify \(\lambda\)

Given the rate of flaws is \(0.08\) per linear foot. So \(\lambda = 0.08\) (average number of flaws per linear foot).

Step3: Identify \(t\)

The interval is \(20\) linear feet. So \(t = 20\) (number of linear - foot units in the interval).

Answer:

\(\lambda=0.08\) and \(t = 20\)