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
marta [7]
2 years ago
12

This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 90 customer orders to fi

ll. Each order requires one component part that is purchased from a supplier. However, typically, 3% of the components are identified as defective, and the components can be assumed to be independent.
Required:
a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?
b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?
c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?
Mathematics
1 answer:
svp [43]2 years ago
3 0

Answer:

a) 0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.

b) 0.4062 = 40.62%  probability that the 100 orders can be filled without reordering components.

c) 0.9034 = 90.34% probability that the 100 orders can be filled without reordering components

Step-by-step explanation:

For each component, there are only two possible outcomes. Either it is defective, or it is not. The components can be assumed to be independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

3% of the components are identified as defective

This means that p = 0.03

a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?

0 defective in a set of 90, which is P(X = 0) when n = 90. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{90,0}.(0.03)^{0}.(0.97)^{90} = 0.0645

0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.

b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?

At most 102 - 100 = 2 defective in a set of 102, so P(X \leq 2) when n = 102

Then

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{102,0}.(0.03)^{0}.(0.97)^{102} = 0.0447

P(X = 1) = C_{102,0}.(0.03)^{1}.(0.97)^{101} = 0.1411

P(X = 2) = C_{102,2}.(0.03)^{2}.(0.97)^{100} = 0.2204

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0447 + 0.1411 + 0.2204 = 0.4062

0.4062 = 40.62%  probability that the 100 orders can be filled without reordering components.

c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?

At most 105 - 100 = 5 defective in a set of 105, so P(X \leq 5) when n = 105

Then

P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{105,0}.(0.03)^{0}.(0.97)^{105} = 0.0408

P(X = 1) = C_{105,0}.(0.03)^{1}.(0.97)^{104} = 0.1326

P(X = 2) = C_{105,2}.(0.03)^{2}.(0.97)^{103} = 0.2133

P(X = 3) = C_{105,3}.(0.03)^{3}.(0.97)^{102} = 0.2265

P(X = 4) = C_{105,4}.(0.03)^{4}.(0.97)^{101} = 0.1786

P(X = 5) = C_{105,5}.(0.03)^{5}.(0.97)^{100} = 0.1116

P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0408 + 0.1326 + 0.2133 + 0.2265 + 0.1786 + 0.1116 = 0.9034

0.9034 = 90.34% probability that the 100 orders can be filled without reordering components

You might be interested in
The ordered pairs in the table below represent a linear function. x y 6 2 9 8 What is the slope of the function? One-fourth One-
Artyom0805 [142]

Answer:

The answer is C) 2

Step-by-step explanation: I hope you get this right also.

8 0
2 years ago
Read 2 more answers
Please help me if you know how! (USAtest prep)
WARRIOR [948]
B.) 24 in
This is because you will divide this shape into 2 rectangles find the area of both of them and then add them together
5 0
2 years ago
Read 2 more answers
PLEASE HELP ME SOLVE THIS ​
klio [65]

Answer:

y = 90°

Step-by-step explanation:

The left side base angle of the triangle and the angle of 110° form a straight angle and are supplementary, thus

base angle = 180° - 110° = 70°

The right base angle is also 70° , thus the triangle is isosceles

The line segment from the vertex is a perpendicular bisector, hence

y = 90°

4 0
3 years ago
The pattern of the scarf is 28 in and 15 in what is the area of the scarf
Soloha48 [4]
The area is 270 inches, because you would do length times width, which in this situation is 28 and 15. You multiply them, and you get 270.
6 0
3 years ago
Read 2 more answers
Tom jogged 3/5 on Monday and 2/6 mile on Tuesday. How much farther did Tom jog on Monday than on Tuesday
natali 33 [55]
You will want to subtract the amount he ran on Monday from the amount on Tuesday. In order to subtract fractions, we must set them to the same denominator (bottom number). In order to do this, we must multiply 3/5 by 6/6 (the denominator on tuesday) which gets us 18/30. Then, for Tuesday, we must multiply 2/6 by 5/5 (the denominator on Monday) which is 10/30. Now, we can do Monday-Tuesday, 18/30-10/30 which gets us 8/30, if we simplify this, we get 4/15 :)
6 0
2 years ago
Other questions:
  • Can somebody help me with this it a little hard
    5·1 answer
  • What is 1(y), when y=-7/12?
    9·1 answer
  • Given: A(-7,8), M(-3,6) find the midpoint
    8·1 answer
  • Find the circumference of the circle.
    12·1 answer
  • An integral equation is an equation that contains an unknown function y(x) and an integral that involves y(x). Solve the given i
    15·1 answer
  • There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the outp
    13·1 answer
  • tucker invested $3500 at 2% interest compounded annually. how much interest will he earn in 3 years? a. $70.00 b. $210.00 c. $21
    8·2 answers
  • <img src="https://tex.z-dn.net/?f=5x%2B7x-1%2F2x%2B1%2F4%3D6%5C%5Cx%3D%3F" id="TexFormula1" title="5x+7x-1/2x+1/4=6\\x=?" alt="5
    6·1 answer
  • Do the math please. i need it nowwwwww
    5·1 answer
  • Which equation would find the distance between the two points show on the coordinate plane?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!