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.

Step 1:
First, let's order the number from least to greatest.
A. -0.31
B. -0.33
C. -0.38
D. -0.29
We could see that A, B, and C's numbers are already from least to greatest, so all we have to do is to move -0.29 (D) up to the top, since -0.29 is the number with the lowest value.
C. -0.38
B. -0.33
A. -0.31
D. -0.29
Step 2:
Let's look at the four number lines. Remember that we already organized the numbers from least to greatest, so the order they go in on the number line is: C, B, A, and D. Since Line C and D Don't follow that rule, we know those are not our answers. Also on line B, C is on the left of -0.4, but C's value is less than -0.4, so B is wrong. We are left with line A.
Line A: C. -0.38, B. -0.33, A. -0.31, D. -0.29
Our answer: Line A
Length of the pie = πD
Length of the pie = 10π
One slice = 10π ÷ 6 = 5.25 in (Answer C)
Answer:
98 - 40√6
Step-by-step explanation:
We have to simplify the following product :
.
Now,
=
=
{Since we know the identity (a - b)² = a² - 2ab + b² }
= 50 - 40√6 + 48
= 98 - 40√6 (Answer)
Answer:
Step-by-step explanation:
to be honest I'm not sure how