EBK INTRODUCTION TO HEALTH PHYSICS, FIF
EBK INTRODUCTION TO HEALTH PHYSICS, FIF
5th Edition
ISBN: 9780071835268
Author: Johnson
Publisher: VST
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Question
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Chapter 9, Problem 9.1P

(a)

To determine

Probability of observing exactly 400 counts in 1 minute.

(a)

Expert Solution
Check Mark

Answer to Problem 9.1P

Probability observing exactly 400, P(n=400) = 0.02

Explanation of Solution

Given:

Mean activity, n¯=400cpm

Number of counts per minute, n = 400 cpm

Formula used:

Standard deviation

  σ=n

Where, n = number of counts

Probability

  p(n)=1σ2πe(nn¯)2/2σ2

Where,

P(n) = probability of finding exactly n

  n¯ = mean activity,

  σ = standard deviation

Calculation:

Standard deviation

  σ=n=400=20

Probability

  p(n)=1σ 2πe (n n ¯ )2/2σ2p(400)=120× 2πe (400400)2/2 (20)2=0.02

Conclusion:

Probability observing exactly 400, P(400) = 0.02

(b)

To determine

Probability of measuring 390 − 410 counts in 1 minute?

(b)

Expert Solution
Check Mark

Answer to Problem 9.1P

Probability of measuring range (390 − 410) counts is 0.383

Explanation of Solution

Given:

Mean activity, n¯=400cpm

Count, n1=390,n2=410

Formula used:

  t=nn¯σ

Where,

t = test

  σ = standard deviation

Calculation:

Test value for 390 counts

  t1=n1n¯σ=39040020=0.5

Test value for 410counts

  t2=n2n¯σ=41040020=0.5

The probability of measuring 390 − 410 counts

  P(390<n<410)=P(0.5<t<0.5)=2[P (t=0.5)0.5]2[0.69150.5]=0.383

Conclusion:

The probability of measuring range (390 − 410)counts is 0.383.

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