1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elixir [45]
3 years ago
5

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

d. a. What is the probability of selecting a carton and finding no defective pens? b. What is the probability of finding eight or more defective pens in a carton? 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? P(x = 0 | λ = 1.2) = b. P(x ≥ 8 | λ = 1.2) = c. P(x > 5 | λ = 1.2) =
Mathematics
1 answer:
nlexa [21]3 years ago
5 0

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

You might be interested in
Find the volume of the prism. 4 in. 8 in. 8 in. ​
Temka [501]

Answer:

256

Step-by-step explanation:

8×8=64

64×4=256

64

4

256

3 0
2 years ago
Read 2 more answers
Is there any app which helps solve pure maths questions?​
allochka39001 [22]

Answer:

math a app good luck with the question

4 0
2 years ago
BRAINLIEST help pls,,,,,,,,,,,,,
icang [17]
Hey there!

1/3 = ?/12

If we observe denominator , it is multiplied by 4

So we must multiple numerator by 4 too

=> 1/3 x 4/4 = 4/12

? = 12.
7 0
2 years ago
Read 2 more answers
Please help ASAP! <br> X= <br><br> A) 4<br> B) 7<br> C) 9
melisa1 [442]

Answer:

C) x = 9

Step-by-step explanation:

When two segments intersect in a circle like so, the product of the two parts of one segment will be equal to the product of the two parts of the other segment.

So,<em> 3 * 6 = x * 2</em>

Multiply: 18 = x * 2

Divide: x = 9

8 0
3 years ago
Read 2 more answers
Which polynomial represents the difference below?
ELEN [110]
I think correct answer if d
6 0
3 years ago
Other questions:
  • A school cafeteria sold 1,280 slices of pizza the first week,640 the second week,and 320 the third week.if this pattern continue
    12·1 answer
  • Solve 2x^2+8x-1=0<br> Using quadratic formula
    8·1 answer
  • Please answer this correctly I want genius expert or ace people to answer this correctly as soon as possible as my work is due t
    15·1 answer
  • There are 4 teams in a basketball league. Each team plays each of the other teams three times. How many games are played?
    11·2 answers
  • uma zelek sells copy paper to local schools. she earns a 13% straight commission on all sales. in november her sales totaled 28,
    7·1 answer
  • A surplus is
    11·2 answers
  • An evergreen nursery usually sells a certain shrub after 7 years of growth and shaping. The growth rate during those 7 years is
    5·1 answer
  • Brainliest to right answer
    6·2 answers
  • Find the area of this acute triangle​
    10·1 answer
  • Casey was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!