Chapter 5: Q.92 (page 356)

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

Expert verified

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

$μ = 3$

Therefore, the decay rate will be:

$m = \frac{1}{μ}$

$= \frac{1}{3}$

$= 0.3333$

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:

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

$= 1 - 0.5134$

$= 0.4866$

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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

Step by step solution

Given Information

Explanation

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What is the probability that a phone will fail within two years of the date of purchase?a.0.8647b. 0.4866c. 0.2212d. 0.9997

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Decision Maths

Applied Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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. $0.9997$