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Problem

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Textbook Expert
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 by,

 

The required probability can be calculated as,

 

Therefore, the probability that a light bulb lasts between six and ten years is,

.

 

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