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Chapter 5: Q.93 (page 356)

What is the median lifetime of these phones (in years)?

a. 0.1941

b. 1.3863

c. 2.0794

d. 5.5452

Short Answer

Expert verified

The correct answer is option (c).

Step by step solution

01

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.

02

Calculation

渭=3

Therefore, the decay rate will be:

m=1渭

=13

=0.3333

It is known that the cumulative distribution function of exponential distribution is,

P(X<x)=1-e-mx.

03

Explanation

It is also known that median is similar to the 50thpercentile of the data. So, calculate the median as below:

P(x鈮�k)=1-e-03mk

0.50=1-e-a.33路

e-0.030x=0.50

Take the logarithmic on both the sides. Then,

lne-0.3333脳k=ln(0.50)

-0.3333脳k=-0.6931

k=2.0794

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