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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

Suppose that the value of a stock varies each day from \(16to\)25with a uniform distribution.

a. Find the probability that the value of the stock is more than \(19.

b. Find the probability that the value of the stock is between role="math" localid="1648188993020" \)19and\(22.

c. Find the upper quartile - 25%of all days the stock is above what value? Draw the graph.

d. Given that the stock is greater than \)18, find the probability that the stock is more than $21.

A random number generator picks a number from one to nine in a uniform manner.

a. X ~ _________

b. Graph the probability distribution.

c. f(x) = _________

d. 渭 = _________

e. 蟽 = _________

f. P(3.5 < x < 7.25) = _________

g. P(x > 5.67)

h. P(x > 5|x > 3) = _________

i. Find the 90th percentile

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)

What is the mean?

What is the area under f(x) if the function is a continuous probability density function?

For a continuous probability distribution, 0鈮�x鈮�15. What is P(x>15)?
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