Question

CCC (Classroom Clicker Co.) produces student response pads. Average normally distributed life span is 500 days; with a known std. dev. of 100 days under normal operating conditions. The company is considering a 300 day warranty for this product (C3). With this warranty policy, what percentage of C3’s sold should we expect to replace under warranty?

2.28%

5.40%

97.72%

4.75%

1.85%

Answer 1

2.28%

Explanation:

Mean life span (μ) = 500 days

Standard deviation (σ) = 100 days

The z-score for any given life span, 'X', is given by the following expression;

`z=(X- \mu)/(\sigma)`

For a 300 day life span, the z-score is:

`z=(300-500)/(100)\\z=-2.0`

According to a z-score table, a z-score of -2.0 falls into the 2.28th percentile of a normal distribution.

Thus, CCC should expect 2.28% of their products sold to be replaced under warranty.