Question

A Poisson distribution with m= 1.2 governs the number of fireflies that flash in a 10 second period during an August evening in the yard. Determine the probability that:

A) 2 fireflies flash

B) Less than or equal 3 flash

C) 6 fireflies flash in a 30 second period

Thanks for help :)

Answer 1

in a Poisson distribution p (X=x)= (

given m= average = = 1.2 per10 sec

a) given x= 2 fireflies flash

p (x=2)=( e^-1.2 × 1.2^2) / 2!

=0.2169

b)x=less than or equal 3 flash

then

p (x3)= p (x=0)+p (x=1)+p (x=2)+p (x=3)

= e^-1.2 [ ]

= 0.30119 [ 1+1.2+ 0.72+0.288]

=0.30119 (3.208)

=0.96623

c) x=6 fireflies flash in a 30 sec period

= 1.2 per 10sec

for 30sec =1.2×3 = 3.6

p (x=6)=

= 0.0826