Question

The average life of a small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If the manufacturer is willing to replace only 3% of the motors that fail, how long a guarantee should he offer? Assume lifetimes are normally distributed.

Answer 1

Answer on Question #73738 – Math – Statistics and Probability

Question

The average life of a small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If the manufacturer is willing to replace only 3% of the motors that fail, how long a guarantee should he offer? Assume lifetimes are normally distributed.

Solution

$$Z = \frac{X - \mu}{\sigma}$$

We have that $\mu = 10, \sigma = 2$.

A z-value of $-1.88$ corresponds to 3% of area under the curve. Then

$$-1.88 = \frac{X - 10}{2}$$

Solve for $X$

$X = 10 - 1.88 \cdot 2 = 6.24$ years (approximately 6 years 88 days).

Answer: 6.24 years.

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