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.

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

Step-by-step 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