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
A standard deck of playing cards contains 52 cards, equally divided among four suits(hearts, diamonds, clubs, and spades). Each
Temka [501]

Answer:

4/17

Step-by-step explanation:

3 0
3 years ago
Betty's bakery bakes white bread and brown bread. The loaves of bread are then stored in a store room that can house only 900 lo
Rainbow [258]
Is this the whole problem?
4 0
3 years ago
Solve the formula for the indicated variable.<br> T(r+s)=rs, for r<br> (Simplify your answer.)
yaroslaw [1]

Answer:

R = \frac{-TS}{(T-S)}

Step-by-step explanation:

First, distribute all terms

T(R+S) =RS\\TR + TS =RS

Get all terms with R onto the same side

TR + TS = RS\\TR - RS = -TS

Factor out the R

R(T-S)=-TS

Divide by (T-S) to isolate R

R = \frac{-TS}{(T-S)}

5 0
3 years ago
Read 2 more answers
I can't seem to find the answer for this I'm pretty sure it's non linear
Nata [24]

Answer:

  (d) No. Slope is not constant.

Step-by-step explanation:

You want to know if the given graph shows a linear function.

<h3>Linear function</h3>

The graph of a linear function is a straight line. The points on the graph shown do not form a straight line, so the function is nonlinear.

<h3>Rate of change</h3>

The rate of change of a function is the ratio of "rise" to "run" between two points in the graph. This ratio is also called the "slope." For a straight line, the rate of change (slope) is constant. That is, a linear function has a constant rate of change.

If the function is nonlinear, its rate of change is not constant. The converse is also true: if the slope is not constant, the function is nonlinear.

6 0
1 year ago
What is the unit rate of $200 for 18ft
sergejj [24]
I hope this helps you




if 18 ft 200$



1 ft ? $



?.18=200.1



?=200/18



?=11,111111
5 0
3 years ago
Other questions:
  • Can someone answer this question please?
    11·1 answer
  • one angle of a triangle measures 120 degrees. the other two angles are congruent. write and solve an equation to find the measur
    5·1 answer
  • Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet,
    15·1 answer
  • There is one pair of congruent triangles in the figure. Identify the congruence using proper notation.
    12·1 answer
  • Follow these steps to apply what you have learned about the angles of a triangle.
    9·2 answers
  • Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 40 cards, which was 4% of the cards sold for M
    11·1 answer
  • A human resource manager is researching the entry-level salary for a technician position. He determined that other companies in
    9·1 answer
  • Distributive property<br> 3(2x – y)
    7·1 answer
  • Rex is currently taking physics as one of his electives in school. His grade at the end of the year is determined by the average
    8·2 answers
  • A book store and a movie theater are 6 kilometers apart along the same street. A florist is located between the bookstore and th
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!