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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

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

modelled by the following distribution:X~Exp(0.2)

Find P(x>6).

Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks).

a. X ~ _________

b. Graph the probability distribution.

c. f(x) = _________

d. ì = _________

e. ó = _________

f. Find the probability that a person is born at the exact moment week 19 starts. That is, find P(x = 19) = _________

g. P(2 < x < 31) = _________

h. Find the probability that a person is born after week 40.

i. P(12 < x|x < 28) = _________

j. Find the 70th percentile.

k. Find the minimum for the upper quarter

Use the following information to answer the next ten questions. The data that follow are the square footage (in 1000feet squared) of 28homes

The sample mean =2.50and the sample standard deviation =0.8302.The distribution can be written as X~U(1.5,4.5).

What type of distribution is this?

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. In words, define the random variable X.

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)

State the probability density function.
See all solutions

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