Question

PLEASE ANSWER! I WILL BRIANLIEST.

Use the bell curve to help answer this question . (attached)
The Boffo Product Company sells a waffle iron on which they have done product testing. They have determined that the amount of time the product will last can be described by a normal distribution. In particular, the average waffle iron lasts for 12 years and one standard deviation is 8 months.

How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time?

Suppose they warranty the waffle iron for the amount of time found in the previous question and suppose that it costs them $13 to make each waffle iron. How much should they charge to make an average profit of $5 per waffle iron? Assume they refund the full price for each failed waffle iron.

Answer 1

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.