Question

In: Statistics and Probability

You can purchase a certain type of resistor from supplier X, Y or Z. The probability...

You can purchase a certain type of resistor from supplier X, Y or Z. The probability of having a faulty resistor if the resistor was bought from supplier X is 0.02; from supplier Y is 0.05; and from supplier Z is 0.1. Your company purchased a total of 1000 resistors: 300 from supplier X, 500 from supplier Y, and 200 from supplier Z. Use this information to answer the following questions.

1.What is the probability that a randomly selected resistor was purchased from supplier Y?(round to 3 decimals)

2.What is the probability that a randomly selected resistor was purchased from supplier X and is faulty? (round to 3 decimals)

3.What is the probability that a randomly selected resistor is faulty? (round to 3 decimals)

4.What is the probability that a randomly selected resistor is not faulty? (round to 3 decimals)

5.Given that a randomly selected resistor is faulty, what is the probability that it was purchased from supplier Y? (round to 3 decimals)

Expert Solution

solution :

total purchases resistors = 1000

purchases from X = 300

from Y = 500

from z = 200

probabilty of defective from X = 0.02, from Y = 0.05, from z =0.1

first of all preparing an contingency table with the given information

	faulty	not faulty	total
X	300*0.02 = 6	294	300
Y	500*0.05 = 25	475	500
Z	200*0.1 = 20	180	200
total	51	949	1000

1)

total resistor purchases from supplier Y = 500

so probability of randomly selected resistor purchases from supplier Y = 500/1000 = 0.5

2)

number of resistor purchases from supplier X and whcich are faulty = 6

so P( purchases from X and faulty ) = 6/1000 = 0.006

3)

total number of resistor which are faulty = 51

so P( faulty ) = 51/1000 = 0.051

4)

total number of resistors which are not faulty = 949

so, P( not faulty ) = 949/1000 = 0.949

5)

it is given that the selected resistor is faulty we have to find the probabilty that it was purchased from Y

total number of faulty resistors = 51

number of faulty resistors in Y = 25

so P(purchases from Y | it is faulty ) = 25/51 = 0.49

orchestra answered 2 years ago

The full three-dimensional Schrödinger equation is −ℏ22m(∂2∂x2ψ(x,y,z)+∂2∂y2ψ(x,y,z)+∂2∂z2ψ(x,y,z))+U(x,y,z)ψ(x,y,z)=Eψ(x,y,z). By using the substitutions from the introduction, this becomes...

The full three-dimensional Schrödinger equation is −ℏ22m(∂2∂x2ψ(x,y,z)+∂2∂y2ψ(x,y,z)+∂2∂z2ψ(x,y,z))+U(x,y,z)ψ(x,y,z)=Eψ(x,y,z). By using the substitutions from the introduction, this becomes −ℏ22m(∂2∂x2ψxψyψz+∂2∂y2ψxψyψz+∂2∂z2ψxψyψz)+(Ux+Uy+Uz)ψxψyψz=Eψxψyψz What is ∂2∂x2ψxψyψz? To make entering the expression easier, use D2x in place of d2ψxdx2, D2y in place of d2ψydy2, and D2z in place of d2ψzdz2. Answer in terms of ψx,ψy,ψz,D2x,D2y,andD2z

The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just...

The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just f (because f is already curried) let f x y z = (x,(y,z)) let f x y z = x (y z)

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )

If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z)...

If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z) b. X×(Y×Z) = (X.Z)Y – (X.Y)Z c. X.(Y×Z) = -Y.(X×Z)

Digital Logic Simplify: F = (x’∙ y’∙ z’) + (x’∙ y ∙ z’) + (x ∙...

Digital Logic Simplify: F = (x’∙ y’∙ z’) + (x’∙ y ∙ z’) + (x ∙ y’ ∙ z’) + (x ∙ y ∙ z) F = (x + y + z’) (x + y’ + z’) (x’ + y + z’) (x’ + y’ + z)

Use two different ways to prove X Y + Z = (X + Z)(Y + Z)....

Use two different ways to prove X Y + Z = (X + Z)(Y + Z). a) Use pure algebraic way b) k-maps

A retailer purchases a certain type of chemical from a supplier on the following quantity discount...

A retailer purchases a certain type of chemical from a supplier on the following quantity discount schedule: • If the order amount is less than 100 kg.s, the supplier charges $30 per kg. • If the order amount is at least 100 kg.s and less than 500 kg.s, the supplier applies an incremental discount where the ﬁrst 100 kg. costs $30 per kg. and the remaining amount costs $28 per kg. • If the order amount is at least 500...

For each of the formulas below, state whether it is true or false. a) pX,Y,Z(x,y,z)=pY(y)pZ∣Y(z∣y)pX∣Y,Z(x∣y,z) ...

For each of the formulas below, state whether it is true or false. a) pX,Y,Z(x,y,z)=pY(y)pZ∣Y(z∣y)pX∣Y,Z(x∣y,z) Select an option True False b) pX,Y∣Z(x,y∣z)=pX(x)pY∣Z(y∣z) Select an option True False c) pX,Y∣Z(x,y∣z)=pX∣Z(x∣z)pY∣X,Z(y∣x,z) Select an option True False d) ∑xpX,Y∣Z(x,y∣z)=1 Select an option True False e) ∑x∑ypX,Y∣Z(x,y∣z)=1 Select an option True ...

Find ??, ?? and ?? of F(x, y, z) = tan(x+y) + tan(y+z) – 1

Let f : X → Y and g : Y → Z be functions. We can...

Let f : X → Y and g : Y → Z be functions. We can deﬁne the composition of f and g to be the function g◦ f : X → Z for which the image of each x ∈ X is g(f(x)). That is, plug x into f, then plug theresultinto g (justlikecompositioninalgebraandcalculus). (a) If f and g arebothinjective,must g◦ f beinjective? Explain. (b) If f and g arebothsurjective,must g◦ f besurjective? Explain. (c) Suppose g◦ f isinjective....