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, 72% are flawless and 28% 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.

Express Y as a function of X.

Find μY

Answer 1

The number of flawless figurines in the sample of size 100 is denoted as X.

The price for flawless figurine is $10, therefore the revenue earned by selling flawless figurine is 10X dollers.

The price for a figurine with minor cosmotic flaws is $3, therefore the revenue earned by selling figurines with minor cosmotic flaws is 3(100-X).

The total revenue earned by selling figurines is denoted as Y.

It is equal to,

10X + 3(100-X) = 7X +300

Thus, Y = 7X + 300

Since 72% of the figurines made by a certain company are flawless , it follows X ~ Bin (100, 0.72). Substituting 100 for n and 0.72 for p into the formula μx = np we find the mean of the random variable X:

μx = 100(0.72) = $72

Now we compute the mean of the random varible Y = 7X+300

μy = μ7x+300 = 7μx+ 300 = (7)(72) + 300 = 804

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