Can someone plz help me with this poisson/binomial problem?

Question

A glass make manufactures sheets of glass, the sheets have faults called seeds that occur randomly and independantly of each other at a rate of 1 per 10m^2.

Find the probability that in a set of 20 sheets each measuring 3.2m by 4m there are exactly 18 sheets with no more than 3 seeds.

Answer 1

ANSWER: BINOMIAL P(18) = 0.151  (15.1% PROBABILITY EXACTLY 18 SHEETS WITH NO MORE THAN 3 SEEDS)

Why???

BINOMIAL PROBABILITY = n! / [r! * (1 - p) ] * p^r * (1 - p)^(n - r)

n = NUMBER OF TRIALS [20]

r = NUMBER OF SUCCESSES [18]  (18 sheets with no more than 3 seeds)

p = PROBABILITY OF SUCCESS [0.958874]

Probability Density Function

Binomial with n = 20 and p = 0.958874

x  P( X = x )

18    0.150902

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

p = PROBABILITY OF SUCCESS - POISSON [rate of 1 per 10m^2]

POISSON DISTRIBUTION, NUMBER OF TIMES AN "EVENT" OCCURS

P(x) = [exp(-λ) * λ^x] / x!

λ = AVERAGE VALUE PARAMETER PER SHEET

λ = [1/(10m^2)] * (3.2 * 4) = 1.28 SEEDS/SHEET

x = NUMBER OF EVENTS [x ≤ 3]

Cumulative Distribution Function

Poisson with mean = 1.28

x  P( X <= x )

3     0.958874