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9 Nov 2021
Given information
Use the following information to answer the next 
exercises. Carbo
is a radioactive element with a half-life of about 
years. Carbon-
is said to decay exponentially. The decay rate is 
We start with one gram of carbon
. We are interested in the time (years) it takes to decay carbon-.
Step-by-step explanation
Step 1.
According to the given information, the random variable 
follows the exponential distribution with parameter 
The cumulative density function of the exponential distribution is given by,
, 
being the decay parameter.
Therefore,
And
Taking logarithm on both sides of the equation:
Therefore, the value of 
such that 
is 
.
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Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 27
- Problem 28
- Problem 29
- Problem 30
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37
- Problem 38
- Problem 39
- Problem 40b
- Problem 41
- Problem 42a
- Problem 43
- Problem 43a
- Problem 43b
- Problem 44
- Problem 45a
- Problem 45b
- Problem 45c
- Problem 46
- Problem 47
- Problem 49
- Problem 50
- Problem 51
- Problem 52
- Problem 53
- Problem 54
- Problem 55
- Problem 56
- Problem 57
- Problem 58
- Problem 59
- Problem 60
- Problem 61
- Problem 62
- Problem 63
- Problem 64
- Problem 65
- Problem 66
- Problem 67
- Problem 68
- Problem 69a
- Problem 69b
- Problem 70a
- Problem 70b
- Problem 71a
- Problem 71b
- Problem 72a
- Problem 72b
- Problem 73
- Problem 74a
- Problem 74b
- Problem 74c
- Problem 74d
- Problem 74e
- Problem 74f
- Problem 74g
- Problem 74h
- Problem 74i
- Problem 74j
- Problem 74k
- Problem 75a
- Problem 75b
- Problem 75c
- Problem 75d
- Problem 75e
- Problem 75f
- Problem 75g
- Problem 75h
- Problem 75h
- Problem 75i
- Problem 76a
- Problem 76b
- Problem 76c
- Problem 76d
- Problem 76e
- Problem 76g
- Problem 76i
- Problem 77a
- Problem 77b
- Problem 77c
- Problem 77d
- Problem 77e
- Problem 77f