Question

The number of knots in a particular type of wood can be modeled by a Poisson distribution with an average of 1.4 knots in 10 cubic feet of the wood. Find the probability that a 20-cubic-foot block of the wood has at most 1 knot.

Answer 1

Probability that a 20- cubic foot block of wood has at most 1 knot P (X<=1) = 0.5918

Explanation:

Average rate of knot= 1.4

Wavelength = 1.4

Geometric probability is given by:

P(X= K) = wavelength ^k × e^-wavelegth

P(X=0) = (1.4^0 × e^-1.4)/0!

P(X=0) = 1 × 0.2466 = 0.2466

P(X=1) = 1.4^1 × e^-1.4

P(X=1)= 1.4×0.2466= 0.3452

P(X<=1)= P(X=0) + P(X=1)

P(X<=1) = 0.2466 + 0.3452 = 0.5918