Textbook ExpertVerified Tutor
17 Nov 2021
Given information
Use the following information to answer the next three exercises. 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.
Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years.
Step-by-step explanation
Step 1.
As given in the problem that the average lifetime of a certain new cell phone is three years. And 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.
Therefore, the random variable is given by,
.
Where 
is the mean.
Now, the decay rate is given by
The cumulative distribution function for the exponential distribution is given as follows:
The required probability can be written as 
and using the complimentary law of probability,
Using the memoryless exponential distribution,
Therefore, the probability is given by
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Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208
Solutions
Chapter
Section
- Problem 74c
- Problem 76f
- Problem 77f
- Problem 77g
- Problem 77h
- Problem 77i
- Problem 78a
- Problem 78b
- Problem 78c
- Problem 78d
- Problem 78e
- Problem 78f
- Problem 78g
- Problem 78h
- Problem 78i
- Problem 79
- Problem 80
- Problem 81
- Problem 82a
- Problem 82b
- Problem 82c
- Problem 82d
- Problem 82e
- Problem 82f
- Problem 82g
- Problem 82h
- Problem 82i
- Problem 82j
- Problem 82k
- Problem 82l
- Problem 83a
- Problem 83b
- Problem 83c
- Problem 83d
- Problem 84a
- Problem 84b
- Problem 85a
- Problem 85b
- Problem 85c
- Problem 85c
- Problem 85d
- Problem 86a
- Problem 86b
- Problem 86c
- Problem 86d
- Problem 86e
- Problem 86f
- Problem 86g
- Problem 86h
- Problem 86i
- Problem 86j
- Problem 87a
- Problem 87b
- Problem 87c
- Problem 87d
- Problem 87e
- Problem 87f
- Problem 87g
- Problem 88a
- Problem 88b
- Problem 88d
- Problem 88e
- Problem 88f
- Problem 88g
- Problem 88h
- Problem 88i
- Problem 89a
- Problem 89b
- Problem 89c
- Problem 89d
- Problem 89e
- Problem 89f
- Problem 89g
- Problem 89h
- Problem 89i
- Problem 90a
- Problem 90b
- Problem 90c
- Problem 90d
- Problem 90e
- Problem 90f
- Problem 91
- Problem 92
- Problem 93
- Problem 94a
- Problem 94b
- Problem 94c
- Problem 94d
- Problem 94e
- Problem 94f
- Problem 94f
- Problem 94g
- Problem 94h
- Problem 95a
- Problem 95b
- Problem 95c
- Problem 95d
- Problem 95e
- Problem 96a
- Problem 96b
- Problem 96c
- Problem 96d
- Problem 96e
- Problem 97a
- Problem 97b
- Problem 97c
- Problem 98a
- Problem 98b
- Problem 98c
- Problem 98d
- Problem 99a
- Problem 99b
- Problem 99c
- Problem 100a
- Problem 100b
- Problem 100c
- Problem 100d
- Problem 101a
- Problem 101b
- Problem 101c
- Problem 101d