Concept explainers
The answer to Exercise 19 part (d) is needed for this exercise. A geologist counts 64 emitted particles in one minute from a certain radioactive rock.
a. Find a 95% confidence interval for the rate of emissions in units of particles per minute.
b. After four minutes, 256 particles are counted. Find a 95% confidence interval for the rate of emissions in units of particles per minute.
c. For how many minutes should errors be counted in order that the 95% confidence interval specifies the rate to within ±1 particle per minute?
a.
Find the 95% confidence interval for the rate of emissions in units of particles per minute.
Answer to Problem 20SE
The 95% confidence interval for the rate of emissions in units of particles per minute is
Explanation of Solution
Given info:
Calculation:
The value of
The value of
From Table A.2 of the Cumulative Normal distribution, the value of
The 95% confidence interval for the rate of emissions in units of particles per minute is,
Thus, the 95% confidence interval for the rate of emissions in units of particles per minute is
b.
Find the 95% confidence interval for the rate of emissions in units of particles per minute.
Answer to Problem 20SE
The 95% confidence interval for the rate of emissions in units of particles per minute is
Explanation of Solution
Given info:
Calculation:
The value of
The value of
From Table A.2 of the Cumulative Normal distribution, the value of
The 95% confidence interval for the rate of emissions in units of particles per minute is,
Thus, the 95% confidence interval for the rate of emissions in units of particles per minute is
c.
Find the number of minutes should errors be counted in order that the 95% confidence interval specifies the rate to within
Answer to Problem 20SE
The number of minutes should errors be counted in order that the 95% confidence interval specifies the rate to within
Explanation of Solution
Calculation:
From Table A.2 of the Cumulative Normal distribution, the value of
The sample size is,
Thus, the number of minutes should errors be counted in order that the 95% confidence interval specifies the rate to within
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Chapter 5 Solutions
Statistics for Engineers and Scientists
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