If (42)P = 414, what is the value of p?<br> 7 8 12 16

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

PLEASE HELP ME????<br> What is the value of the expression below? A. 8 B. 4 C. 1 D. 2

shutvik [7]

I did this in london! Its B. 4 For londons answers! by mate!

4 0

2 years ago

Suppose the population of a town is 98,000 in 2014. The population increases at a rate of 3.7 percent every year. What will the

Setler [38]

Answer: 121871

Step-by-step explanation:

Current population = 98000

Rate of increase = 3.7% / year

Total time = 2020 - 2014 = 6 years

Population in 2020 = 98000 * (1+ (3.7/100))^6

= 98000 * (1.037)^6 = 98000 * 1.243576 = 121870.505

Rounding off to nearest whole number we get the population = 121871

3 0

3 years ago

If a circle has circumference 100pi units, what is it’s area

const2013 [10]

Answer:

2500pi^2 units

Step-by-step explanation:

Circumference = pi * diameter

Circumference = pi * 100

Radius = diameter/2

Radius = 50

Area = pi * radius^2

Area = pi * 50^2

Area = pi * 2500

Area = 2500pi^2 units

8 0

2 years ago

Abdul flips a weighted coin 64 times and gets 16 tails. Based on experimental probability, how many of the next 40 flips should

sergij07 [2.7K]

Answer:

yes, Abdul should expect to come up tails.

7 0

3 years ago

If (42)P = 414, what is the value of p? 7 8 12 16​

If (42)P = 414, what is the value of p? 7 8 12 16