Concept explainers
Unifrom Distribution: Measurement Errors Measurement errors from instruments are often modeled using the uniform distribution (see Problem 12). To determine the
(a) less than +0.03 microsecond
(c) between -0.04 and +0.01 microsecond?
(d) Find the
(a)
To find: Theprobability thatsuch measurements will be in error byless than 0.03 microseconds.
Answer to Problem 13P
Solution: Theprobability that such measurements will be in error byless than 0.03 microsecondsis0.8.
Explanation of Solution
Calculation:
Let
Let x is chosen at random from [
We have to find the probability of less than 0.03 microseconds,
Hence,
(b)
To find: Theprobability thatsuch measurements will be in error bymore than -0.02 microseconds.
Answer to Problem 13P
Solution: Theprobability that such measurements will be in error by more than -0.02 microsecondsis0.7.
Explanation of Solution
Calculation:
Let
Let x is chosen at random from [
We have to find the probability of more than -0.02 microseconds,
Hence,
(c)
To find: Theprobability thatsuch measurements will be in error bybetween -0.04 and 0.01 microseconds.
Answer to Problem 13P
Solution: Theprobability that such measurements will be in error bybetween -0.04 and 0.01 microsecondsis0.5.
Explanation of Solution
Calculation:
Let
Let x is chosen at random from [
We have to find the probability between -0.04 and 0.01 microseconds,
Hence,
(d)
To find: Themean and standard deviation of measurement errors and whether the measurements for these acoustical sensors are unbiased.
Answer to Problem 13P
Solution:
The mean of measurement errors is 0. The standard deviation of measurement errors is 0.029. Yes, the measurements for these acoustical sensors are unbiased.
Explanation of Solution
Calculation:
Let
We have to find the mean,
Therefore, the mean is 0 microsecond.
We have to find the standard deviation,
Therefore, thestandard deviationis 0.029microsecond.
Yes, since the obtained mean of the measurement errors is zero so the measurements for these acoustical sensors are unbiased.
Want to see more full solutions like this?
Chapter 7 Solutions
Understanding Basic Statistics
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill