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Homework #3
ME 236
I. Review Questions (Not Due)
1. True or False:
a. All random measurements are normally distributed.
b. Using the z value in confidence intervals presumes that the population standard
deviation is known.
c. Approximately 92% of all data in a normal distribution lie within ±1.75 standard
deviations from the population mean.
When predicting the mean of a population based on the mean of a sample (the population
standard deviation is known), what happens to the confidence interval when the sample
size approaches infinity? Circle all that apply:
a. the confidence interval approaches a finite value
b. the confidence interval approaches zero
c. the z value approaches 1.96
d. the confidence interval approaches infinity
3. Evaluate the integral: f ( x) 
6 0.5 x 2
dx . Hint: e a b  e a e b . Do so without any integration
functions on your calculator.
II. Homework (Due)
Turn in the following 4 problems from the book, plus the extra Problem 3-A below.
3-2, 4, 6, 8, 10
Problem 3-A. A voltmeter is used to measure a known voltage of 100 V. Forty percent of the
readings are within 0.5 V of the mean value.
a. Assuming a normal distribution for the error, estimate the standard deviation for the
b. What is the probability that the mean of 10 readings will have an error greater than 0.75