Hi,

I have two probability problems and I need them to be checked please:

problem-1

A company makes plastic panel used in automobiles. The panel production process is such thast the number of flaws on a panel follows a Poisson process with a mean of 0.03 flaws per panel.

1-If one panel is randomly selected from the production process, what is the probability it has no flaws.

My solution:

lambda=0.03*1=0.03

f(0,0.03)=(e^(-0.03)*(0.03)^0)/(0!)

2-if 50 panesl is randomly sampled from the production process, what is the probability it has no flaws.

No solution here. I am not sure but it is the same as above but with lambda=0.03*50??

3-What is the expected number of panels that need to be sampled before flaws are found?

I am not sure of what I have done for this question:

lambda=0.03

(0.03)*n=1----->n=33.33 for one flaw.so 2 falws-->n=66.66

problem 2

the probability is 0.6 that a well driller will find a well of water at a depth less than 100 feet in a certain area. Wells are to be drilled for six new homeowners. Assue that finding a well of water at a depth of less than 100 feet is independent from drilling to drilling and that the probability is 0.6 on every drilling. If X is the number of wells of water found. Find:

1-P(X>4)

My solution: P(X>4)=1-B(4;6,0.6)

2-P(X=4)

P(X=4)=b(4;6,0.6)

3-mean

mean=n*p=3.6

4-variance

Var^2=n*p*(1-p)

5-P(X=mean)

Here since mean =3.6, I have problem to find P(X=mean)

B.