235+123= solve using a number line

A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distribute

nlexa [21]

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:

$P(k)=\frac{\lambda^{k}e^{-\lambda}}{k!}= \frac{1.2^{k}\cdot e^{-1.2}}{k!}$

a. What is the probability of selecting a carton and finding no defective pens?

This happens for k=0, so the probability is:

$P(0)=\frac{1.2^{0}\cdot e^{-1.2}}{0!}=e^{-1.2}=0.301$

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.

$P(k\geq8)=1-P(k$

$P(0)=1.2^{0} \cdot e^{-1.2}/0!=1*0.3012/1=0.301\\\\P(1)=1.2^{1} \cdot e^{-1.2}/1!=1*0.3012/1=0.361\\\\P(2)=1.2^{2} \cdot e^{-1.2}/2!=1*0.3012/2=0.217\\\\P(3)=1.2^{3} \cdot e^{-1.2}/3!=2*0.3012/6=0.087\\\\P(4)=1.2^{4} \cdot e^{-1.2}/4!=2*0.3012/24=0.026\\\\P(5)=1.2^{5} \cdot e^{-1.2}/5!=2*0.3012/120=0.006\\\\P(6)=1.2^{6} \cdot e^{-1.2}/6!=3*0.3012/720=0.001\\\\P(7)=1.2^{7} \cdot e^{-1.2}/7!=4*0.3012/5040=0\\\\$

$P(k$

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.

$P(k>5)=1-P(k\leq5)=1-\sum_{k=0}^5P(k)\\\\P(k>5)=1-(0.301+0.361+0.217+0.087+0.026+0.006)\\\\P(k>5)=1-0.998=0.002$

5 0

3 years ago

41 percent of 78 is what?

lisabon 2012 [21]

Answer:

31.98

Step-by-step explanation:

78 * .41 = 31.98

5 0

3 years ago

Read 2 more answers

Sages team needs to buy at least 75 cans, but they only have $50 to spend.Use the information sages collected to find another op

serious [3.7K]

You will have 13 cans left over.

4 0

3 years ago

Read 2 more answers

Please guys i really need your help and please explain how you got it please

lina2011 [118]

The answer would be C because in order to find the area of a figure, you would need to multiply its height by its width. finding the area of a figure is the same as finding how many units are in a figure. because this is a square and all the sides are equal, by counting the total number of units, you can find the area.

5 0

3 years ago

How to Evaluate 5/9 x 8

GuDViN [60]

Answer:

4 4/9

Step-by-step explanation:

First, you have to set it up: 5/9 times 8/1

We made it 8/1 since it has to be a fraction in the multipying ocess and the one does not change the value.

Next, Multiply.

5/9x8/1=40/9 as an inproper fraction

As a proper fraction, it is written as 4 4/9

3 0

2 years ago