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(Continues Exercise 20 in Section 4.11.) The age of an

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 11E Chapter 4.12

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 11E

Problem 11E

(Continues Exercise 20 in Section 4.11.) The age of an ancient piece of organic matter can be estimated from the rate at which it emits beta particles as a result of carbon-14 decay. For example, if X is the number of panicles emitted in 10 minutes by a 10,000-year-old bone fragment that contains 1 g of carbon, then X has a Poisson distribution with mean  λ= 45.62. An archaeologist has found a small bone fragment that contains exactly 1 g of carbon. If t is the unknown age of the bone, in years, the archaeologist will count the number X of particles emitted in 10 minutes and compute an estimated age ? with the formula

Unknown to the archaeologist, the bone is exactly 10,000 years old, so X has a Poisson distribution with λ = 45.62.

a. Generate a simulated sample of 1000 values of X, and their corresponding values of  

b. Estimate the mean of .

c. Estimate the standard deviation of .

d. Estimate the probability that will be within 1000 years of the actual age of 10,000 years.

4.12 Simulation 317

e. Estimate the probability that  will be more than 2000 years from the actual age of 10,000 years.

f. Construct a normal probability plot for . Is   approximately normally distributed?

Step-by-Step Solution:

Solution:

Step 1 of 4:

  Let X is the number of beta particle emitted in 10 minutes by 10,000 year old bone fragment . X has a poisson distribution with mean = 45.62. The age of an ancient piece will estimated by using the formula  

                           =  


Step 2 of 4

Chapter 4.12, Problem 11E is Solved
Step 3 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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(Continues Exercise 20 in Section 4.11.) The age of an