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Chapter 5: Q. 68 (page 351)

Carbon-14 is a radioactive element with a half-life of about

5,730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121. We start with one gram of carbon-14.

We are interested in the time (years) it takes to decay carbon-14. The distribution for X is ______.

Short Answer

Expert verified

This distribution for X is an exponential distribution.

Step by step solution

01

 Definition of exponential distribution

Exponential distribution is a time probability distribution that depends between any kind of events in a Poisson process.

In this case of Poisson Process is a model series of discrete event. Here the average time between event is known but exact time is unknown.

02

Justification of exponential distribution 

Here in this scenario Carbon-14 is decaying exponentially.

As the carbon-14 is decreasing exponentially, thus the random distribution mass variable of carbon-14 (X) is conveyed through "exponential distribution".

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Most popular questions from this chapter

Suppose the time it takes a student to finish a quiz is uniformly distributed between six and 15 minutes, inclusive. Let X=the time, in minutes, it takes a student to finish a quiz. Then X~U(6,15)Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. Then find the probability that a different student needs at least eight minutes to finish the quiz given that she has already taken more than seven minutes.

Carbon-14 is a radioactive element with a half-life of about

5,730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121. We start with one gram of carbon-14.

We are interested in the time (years) it takes to decay carbon-14. What is the decay rate (m)?

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 m? What does it represent?

On average, a pair of running shoes can last 18 months if used every day. The length of time running shoes last is exponentially distributed. What is the probability that a pair of running shoes last more than 15 months? On average, how long would six pairs of running shoes last if they are used one after the other? Eighty percent of running shoes last at most how long if used every day?

Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. Find the average age of the cars in the lot.
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