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Porcelain figurines are sold for $10 if flawless, and for
Chapter 4, Problem 23E(choose chapter or problem)
Porcelain figurines are sold for $10 if flawless, and for $3 if there are minor cosmetic flaws. Of the figurines made by a certain company, 90% are flawless and 10% have minor cosmetic flaws. In a sample of 100 figurines that are sold, let \(Y\) be the revenue earned by selling them and let \(X\) be the number of them that are flawless.
a. Express \(Y\) as a function of \(X\).
b. Find \(\mu_{Y}\).
c. Find \(\sigma_{Y}\)
Equation Transcription:
Text Transcription:
Y
X
mu Y
sigma Y
Questions & Answers
QUESTION:
Porcelain figurines are sold for $10 if flawless, and for $3 if there are minor cosmetic flaws. Of the figurines made by a certain company, 90% are flawless and 10% have minor cosmetic flaws. In a sample of 100 figurines that are sold, let \(Y\) be the revenue earned by selling them and let \(X\) be the number of them that are flawless.
a. Express \(Y\) as a function of \(X\).
b. Find \(\mu_{Y}\).
c. Find \(\sigma_{Y}\)
Equation Transcription:
Text Transcription:
Y
X
mu Y
sigma Y
ANSWER:Solution 23E
Step1 of 4:
We have a random variable X it presents the the number of them that are flawless in a sample 100 and a random variable Y is the revenue earned by selling them. The price of the flawless figurines $10 Then the revenue earned by selling flawless figurines is 10X dollars.
The price of the minor cosmetic flaws is $3. Then the revenue earned by selling figurines with minor cosmetic flaws is 3(100 - X).
Here our goal is:
a).We need to express Y as a function of X.
b).We need to find
c).We need to find
Step2 of 4:
a).
From the given information we have The price of the flawless figurines $10.
The revenue earned by selling flawless figurines is 10X dollars.
The price of the minor cosmetic flaws is $3.
The revenue earned by selling figurines with minor cosmetic flaws is 3(100 - X).
Then,
Y can be expressed as Y = (The revenue earned by selling flawless figurines) + (The revenue
earned by selling figurines with minor cosmetic flaws)
= (10X) + 3(100 - X)
= 10X + 300 - 3X
&