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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

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

Explanation

渭=3

Therefore, the decay rate will be:

m=1渭

=13

=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鈮�2)=1-e0.333-2

=1-0.5134

=0.4866

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Most popular questions from this chapter

The number of days ahead travelers purchase their airline tickets can be modeled by an exponential distribution with the average amount of time equal to 15 days. Find the probability that a traveler will purchase a ticket fewer than ten days in advance. How many days do half of all travelers wait?

Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X~Exp(0.2)

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A distribution is given as X~U(0,20). What is P(2<x<18)? Find the90thpercentile.

98. During the years 1998-2012, a total of 29 earthquakes of magnitude greater than 6.5 have occurred in Papua New Guinea. Assume that the time spent waiting between earthquakes is exponential.

a. What is the probability that the next earthquake occurs within the next three months?

b. Given that six months have passed without an earthquake in Papua New Guinea, what is the probability that the next three months will be free of earthquakes ?

c. What is the probability of zero earthquakes occurring in 2014?

d. What is the probability that at least two earthquakes will occur in 2014 ?

The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x)=120 where X goes from 25 to 45 minutes.

a. Define the random variable. X=

b. X~

c. Graph the probability distribution.

d. The distribution is (name of distribution). It is (discrete or continuous).

e. 渭=

f. 蟽=

g. Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.

h. Find the probability that the time is between 30 and 40 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.

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j. Find the 90th percentile. This means that 90% of the time, the time is less than

k. Find the 75th percentile. In a complete sentence, state what this means. (See part j.)

1. Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.
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