how to estimate in how much time will they return lightbulbs

I. The Readylite Company produces a flashlight in which product managers are trying to decide how long a warranty to issue.

If the managers believe the life of the flashlight follows a normal distribution with a mean of 3.5 years and a standard deviation of 1.50 years):

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a. What percentage of flashlights sold can they anticipate will be returned within the first one and one-half years?

b. What percentage of flashlights sold can they anticipate will be returned within two and one-half years?

c. What percentage of flashlights sold can they anticipate will be returned between the first one and one-half and three and one-half years?

II. Suppose a company has a design maximum output of 280. Its actual output is 195 and its efficiency is 80%. Calculate its effective output and its capacity utilization.

III. Suppose a company has a fixed cost of $140,000 and a variable cost per unit of $9. It sells its product for $14.

a. Calculate its break-even level of output.

b. Calculate how much it must produce to make $145,000, assuming it can sell it all.

Extra credit – 15 points. If it can outsource, and buy the product wholesale from a distributor at $11 each, over what level of output should it buy from the wholesaler, and over what level should it produce on its own?