Answer:
a. P(x = 0 | λ = 1.2) = 0.301
b. P(x ≥ 8 | λ = 1.2) = 0.000
c. P(x > 5 | λ = 1.2) = 0.002
Step-by-step explanation:
If the number of defects per carton is Poisson distributed, with parameter 1.2 pens/carton, we can model the probability of k defects as:

a. What is the probability of selecting a carton and finding no defective pens?
This happens for k=0, so the probability is:

b. What is the probability of finding eight or more defective pens in a carton?
This can be calculated as one minus the probablity of having 7 or less defective pens.



c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than five defective pens. What is the probability that a carton contains more than five defective pens?
We can calculate this as we did the previous question, but for k=5.

Answer:

Step-by-step explanation:
Solving
:

F(x)=7x-1/2
Add the half to the other side afeterreplacing f(x) with a zero
1/2=7x divide by 7
7/2=x, when y=0
Answer: 6.48
Step-by-step explanation:
Mean is 79.4, population size is 5
MAD formular is addition of variance point /population size
n∑∣xi−xˉ∣
F(x)= x+13
F(-2)= -2 +13
= 11
You plug in -2 for the x