Question

An article reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2500 individuals, what is the approximate distribution of the number who carry this gene? 

We can approximate this distribution by the Poisson distribution with μ = _______  

(a) Use the Poisson approximation to calculate the approximate probability that between 4 and 10 (inclusive) carry the gene.  

(b) Use the Poisson approximation to calculate the approximate probability that at least 10 carry the gene. 

Answer 1

a)

P(4<=X<=10)=

∑x=x1x2   {e-λ*λx/x!}=

0.721

Note:

if using ti-84 use commannd :poissoncdf(5,10)-poissoncdf(5,3)

if using excel use commannd :poisson(10,5,true)-poisson(3,5,true)

b)

P(X>=10)=1-P(X<=9)=

1-∑x=0x e-λ*λx/x!=

0.0318

Note:

if using ti-84 use command :1-poissoncdf(5,9)

if using excel use commannd :1-poisson(9,5,true)