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
34kurt
3 years ago
14

A machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%). Prior to shipm

ent produced parts are passed through an automatic inspection machine, which is supposed to be able to detect any part that is obviously defective and discard it. However, the inspection machine is not perfect. A part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input. Slightly defective parts are marked as defective and discarded 40% of the time, and obviously defective parts are correctly identified and discarded 98% of the time.
Required:
a. What is the total probability that a part is marked as defective and discarded by the automatic inspection machine?
b. What is the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped?
c. What is the probability that a part is 'bad' (obviously defective) given that it makes it through the inspection machine and gets shipped?
Mathematics
1 answer:
AURORKA [14]3 years ago
5 0

Answer:

(a) 0.0686

(b) 0.9984

(c) 0.0016

Step-by-step explanation:

Given that a machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%).

Let A, B, and C be the events of defect-free, slightly defective, and the defective parts produced by the machine.

So, from the given data:

P(A)=0.90, P(B)=0.03, and P(C)=0.07.

Let E be the event that the part is disregarded by the inspection machine.

As a part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input.

So, P\left(\frac{E}{A}\right)=0.02

Now, from the conditional probability,

P\left(\frac{E}{A}\right)=\frac{P(E\cap A)}{P(A)}

\Rightarrow P(E\cap A)=P\left(\frac{E}{A}\right)\times P(A)

\Rightarrow P(E\cap A)=0.02\times 0.90=0.018\cdots(i)

This is the probability of disregarding the defect-free parts by inspection machine.

Similarly,

P\left(\frac{E}{A}\right)=0.40

and \Rightarrow P(E\cap B)=0.40\times 0.03=0.012\cdots(ii)

This is the probability of disregarding the partially defective parts by inspection machine.

P\left(\frac{E}{A}\right)=0.98

and \Rightarrow P(E\cap C)=0.98\times 0.07=0.0686\cdots(iii)

This is the probability of disregarding the defective parts by inspection machine.

(a) The total probability that a part is marked as defective and discarded by the automatic inspection machine

=P(E\cap C)

= 0.0686 [from equation (iii)]

(b) The total probability that the parts produced get disregarded by the inspection machine,

P(E)=P(E\cap A)+P(E\cap B)+P(E\cap C)

\Rightarrow P(E)=0.018+0.012+0.0686

\Rightarrow P(E)=0.0986

So, the total probability that the part produced get shipped

=1-P(E)=1-0.0986=0.9014

The probability that the part is good (either defect free or slightly defective)

=\left(P(A)-P(E\cap A)\right)+\left(P(B)-P(E\cap B)\right)

=(0.9-0.018)+(0.03-0.012)

=0.9

So, the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped

=\frac{\text{Probabilily that shipped part is 'good'}}{\text{Probability of total shipped parts}}

=\frac{0.9}{0.9014}

=0.9984

(c) The probability that the 'bad' (defective} parts get shipped

=1- the probability that the 'good' parts get shipped

=1-0.9984

=0.0016

You might be interested in
Solve for x. x = [?] 5x - 7/3x + 27 ..​
ArbitrLikvidat [17]

Answer:

x = 20

Step-by-step explanation:

the angles shown are supplementary

supplementary angles add up to 180°

hence, 5x - 7 + 3x + 27 = 180

==> combine like terms

8x + 20 = 180

==> subtract 20 from both sides

8x = 160

==> divide both sides by 8

x = 20

3 0
2 years ago
If cotton candy sells for $4 per bag and the booth is
Kryger [21]

Answer:

Here ya go ! :)

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
-<br> What is g(x)= -4(x - 5)2 + 8 in standard form
Ulleksa [173]

Answer:

g(x) = -8x + 48

4 0
2 years ago
You believe that eating an apple a day is healthy and want to design an experiment to find out. You have available 40 volunteers
Gwar [14]

The best design for this experiment would be a repeated measures design. This is ideal to determine if eating an apple makes you healthy.

<h3>What is an experimental design?</h3>

An experimental design refers to the general structure of an experiment including how people are distributed into the control and experimental group to test a specific phenomenon.

<h3>What is a repeated measures design?</h3>

In a repeated measures design all participants are both parts of the control group, in this case, people who do not eat apples, and the experimental group, or people who eat apples.

<h3>What does this design imply?</h3>

In the case of determining if eating an apple every day, this design implies:

  • All participants will be asked to not eat apples every day for a specific period such as one or two months, and health levels will be measured during this time.
  • After the first step, all participants will be asked to eat an apple every day during the period, and their health will be measured.
  • The researcher can compare the results of each participant, which is more accurate than comparing one participant to another.

Learn more about experiments in: brainly.com/question/1452319

7 0
2 years ago
Is a half bigger then a third ?
Assoli18 [71]


1/2 plus 1/3 is 5/6.

You have to find the common denominator

7 0
3 years ago
Read 2 more answers
Other questions:
  • Help please don’t know this !
    11·2 answers
  • How can graphing be applied to solving systems of nonlinear equations?
    8·1 answer
  • Simplify 8 - {x - (5 + x)}
    15·2 answers
  • Find the second derivative of r(x)=10x-0.001x^2​
    8·1 answer
  • Suppose I work on a factory line doing quality control work. Since I've been working here for such a long time, I am fairly conf
    14·1 answer
  • PLS HELP ME !
    8·1 answer
  • Find BD ( I need to find this answer quick )
    11·1 answer
  • 2х – у = 7<br>3х + y = 3​
    5·2 answers
  • What value of x make the equation 24-(3x - 9)-6= -2(4x - 10+ 5x + 7 true?
    9·1 answer
  • Which characteristics are appropriate for the Brand of camcorder? Choose all that apply
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!