Question

What is the probability that a phone will fail within two years of the date of purchase?

a.$0.8647$

b. $0.4866$

c. $0.2212$

d. $0.9997$

Short answer

The correct answer is Option (b).

Step-by-step solution

Given Information

The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.

Explanation

$\mu =3$

Therefore, the decay rate will be:

$m=\frac{1}{\mu }$

$=\frac{1}{3}$

$=0.3333$

It is known that the cumulative distribution function of the exponential distribution is, $P(X<x)=1-e^{-m}$.

The required probability can be calculated as below:

$P(x\le 2)=1-e^{0.333-2}$

$=1-0.5134$

$=0.4866$