Question

Please use excel to solve!

(1) Environmental concerns regarding the release of warm water into a Great Lake led to the sampling of zoo plankton Cyclops. The expected number of Cyclops follows a Poisson distribution with a expected number of 3.2 per 200cc of water. Let X represent the number of plankton. Find :

(a) P(X = 4)

(b) P(X ≥ 6) in 400 cc of water

(c) P(3 ≤ X ≤ 7)

(d) Find µX.

(e) Find σX

Answer 1

Given

(a) P(X = 4)  =

P(X = 4) = 0.178093

for 400cc

p(x=0)	0.001661557
p(x=1)	0.010633967
p(x=2)	0.034028693
p(x=3)	0.072594545
p(x=4)	0.116151272
p(x=5)	0.148673628
total=	0.383743662
p(x>= 6)=	1-0.383744
	0.616256338

c) P(3 ≤ X ≤ 7) for mean

p(x=3)	0.222616
p(x=4)	0.178093
p(x=5)	0.113979
p(x=6)	0.060789
p(x=7)	0.027789
	0.603266

d) Find µX.= 3.2

(e) Find σX =sqrt (3.2)

=1.78885