Question

The average number of rare flowers in a 2-acre field is estimated to be 17 per acre. Find the probability that at most 13 rare flowers are found on (a) A given acre (b) On at least 4 of the next 10 acres inspected

Answer 1

this is Poisson distribution with parameter λ=rare flower in one acre =17/2=8.5

a)probability that at most 13 rare flowers are found on A given acre

P(X<=13)=

∑x=013 {e-8.5*8.5x/x!}=

0.9486

(note:

if using ti-84 use commannd :poisson(8.5,13)

if using excel use commannd :poisson(13,8.5,true)

b)next 10 acres:

here this is binomial with parameter n=10 and p=0.9486

P( at least 4 of the next 10 acres inspected):

P(X>=4)=1-P(X<=3)=

1-∑x=03   (10Cx)0.9486x(1-0.9486)(10-x) =

~1.0000:

if using ti-84 use command :1-binomcdf(10,0.9486,3)
if using excel use command :1-binomdist(3,10,0.9486,true)