Question

A critical characteristic of our product is what is known as the "shelf life", since its expiration date and the costs related to the guarantees depend on it. Historical data shows that the "shelf life" of my product has a Normal behavior with an average of 20 months and a standard deviation of 1.5 months. What time must elapse between the date the product is manufactured and the expiration date on the label if we want no more than 0.5% to be defective by that date? In other words, how much time do we have to sell the product if we want 99.5% to reach the customer in good condition?

Answer 1

Let x be the shelf life of a product.

x follows normal distribution with

Mean ( μ ) = 20 months and

Standard deviation ( σ) = 1.5 months

We want no more than 0.5% of the product to be defective.

That means area under the normal curve in the left tail is 0.005 .

Using z table , value of z score corresponding to area 0.005 is -2. 575

Therefore z = - 2.575

z = ( x - μ) / σ

Therefore x = z σ + μ

x = ( -2. 575) (1.5) + 20

x = 16.1375

x = 16.14

Therefore the time elapsed between the manufacturing date and the expiration date is 16.14 months.