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Mathematics

1 answer:

Brut [27]3 years ago

5 0

Let x be the required waranty period, then
P(X < x) = P(z < (x - 12)/(8/12)) = 1 - 0.067 = 0.933
P(z < 12(x - 12)/8) = P(z < 1.498)
12(x - 12)/8 = 1.498
x - 12 = 8(1.498) / 12 = 0.9987
x = 12 - 0.9987 = 11

Therefore, they should waranty for 11 years so that no more than 6.7% fail within that time.

cost of production = %13
Let the price be p, then
revenue less price of failed iron = p - 0.067(13) = p - 0.871
Profit = p - 0.871 - 13 = 5
p - 13.871 = 5
p = 5 + 13.871 = 18.871

Therefore, the should charge $18.87 per waffle iron.

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$P(Y_1$

(I leave the details of the second integral to you)

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