Question

On average, there are 17 dandelions for every 5 square metres in a large field.
a) If you select a random 5 square metre section of this field, what is the probability that you will find 10
dandelions?
b) If you select a random 3 square metre section of this field, what is the probability that you will find 8
dandelions?

Answer 1

a) For Poisson distribution,

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!}$

Given,

$\lambda=17$

$x=10$

$P(X=10)=\frac{e^{-17}*17^{10}}{10!}$

$P(X=10)=0.0230$

b) For 1 square metre, average number of dandelions= 17/5 =3.4

For 3 square metres, average number of dandelions=(3*3.4)=10.2

  $\lambda=10.2$

  $x=8$

$P(X=8)=\frac{e^{-10.2}*(10.2)^{8}}{8!}$

$P(X=8)=0.1080$