Concept explainers
a.
Find the value of
a.
Answer to Problem 18E
The value of
Explanation of Solution
Given info:
The mean decay rate of radioactive mass is at least 1 particle per second. If the mean decay rate is less than 1 per second, then the product will return for a refund. The number of decay events counted in 10 seconds is denoted as X.
Calculation:
The random variable X is defined as the number of decay events counted in 10 seconds. The X follows Poisson with mean,
The Poisson distribution formula is,
Where, x is a non-negative integer,
The required probability is
Substitute x as 0, 1,
Thus, the required probability is,
b.
Check whether one
b.
Answer to Problem 18E
Yes, one event in 10 seconds be an unusually small number.
Explanation of Solution
Justification:
From part (a), the value of
Thus, the one event in 10 seconds is an unusually small number.
c.
Explain whether counted one decay event in 10 seconds would be convincing evidence that the product should be returned or not.
c.
Answer to Problem 18E
Yes. Since one event in 10 seconds is an unusually small number.
Explanation of Solution
Justification:
From part (b), it clear that one event in 10 seconds is an unusually small number. Thus, it can be concluded that one decay event in 10 seconds would be convincing evidence that the product should be returned.
d.
Find the value of
d.
Answer to Problem 18E
The value of
Explanation of Solution
Calculation:
The random variable X is defined as the number of decay events counted in 10 seconds. The X follows Poisson with mean,
The required probability is
Substitute x as 0, 1,
Thus, the required probability is,
e.
Check whether 8 events in 10 seconds be an unusually small number, if the mean decay rate is 1 particle per second.
e.
Answer to Problem 18E
No. Since about
Explanation of Solution
Justification:
From part (d), the value of
Thus, the 8 events in 10 seconds is not an unusually small number.
f.
Explain whether counted 8 decay events in 10 seconds would be convincing evidence that the product should be returned or not.
f.
Answer to Problem 18E
No. Since 8 events in 10 seconds is not an unusually small number.
Explanation of Solution
Justification:
From part (e), it clear that 8 events in 10 seconds is not an unusually small number. Thus it can be concluded that 8 decay events in 10 seconds would not be convincing evidence that the product should be returned.
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Chapter 4 Solutions
Statistics for Engineers and Scientists (Looseleaf)
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