When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 979,280 radioactive atoms, so 20,720 atoms decayed during 365 days. The probability that on a given day, 50 radioactive atoms decayed, is (round to six decimal places)
When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 979,280 radioactive atoms, so 20,720 atoms decayed during 365 days. The probability that on a given day, 50 radioactive atoms decayed, is (round to six decimal places)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 27T
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Question
When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 979,280 radioactive atoms, so 20,720 atoms decayed during 365 days.
The probability that on a given day, 50 radioactive atoms decayed, is (round to six decimal places)
Expert Solution
Step 1
The given problem follows a Poisson distribution
f(x) = ; x=0, 1,2....
The mean no. of radioactive atoms decayed in a day, = = 56.76 atoms per day
Therefore, P( 50 atoms will decay in a given day) =
= 0.037024
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