Quiz #6
Semester 041
Instructor: Dr. Mohammad H. Omar
Stat319: Intro to Prob & Stat for Engineers & Scientists Section: 2 (8-8.50am) 4(9-9.50am)
Name:_______________________ ID#:______________ Serial #:_____________________
Directions: There are two questions you must answer to obtain a total of 10 points for this quiz. If
your ID ends with an even number, answer questions 1 and 2. If your ID is odd, answer questions 1 and
3. The last question is optional and is provided as a bonus.
1. [5 pts] Runger and Pignatiello (1991) consider a plastic injection molding process for a steel part
that has a critical width dimension with a historic standard deviation of 8. Periodically, clogs form
in one of the feeder lines, causing the mean width to change. As a result, the operator periodically
takes random samples of size four
a. A recent sample yielded a sample mean of 101.4. Construct a 99% confidence interval
for the true mean width.
b. Find the sample size required to estimate the true mean width to within +2 units using a
99% confidence interval.
c. If the inspector took 1000 different samples of size 4 over the cause of the year and construct
99% confidence interval each time, how many of these intervals will contain the true mean?
2. [5 pts] The modulus of rupture (MOR) for a particular grade of pencil lead is known to have a
standard deviation of 250 psi.
a. A random sample of 16 pencil leads yielded a sample mean of 6490. Construct a 90%
confidence interval for the true mean MOR.
b. Explain the meaning of the confidence interval you obtained in (a) in the context of the question.
c. Find the sample size required to estimate the true mean MOR to within +l00 using a
90% confidence interval.
3. [5 pts] Yashchin (1995) discusses a process for the chemical etching of silicon wafers used
integrated circuits. This process etches the layer of silicon dioxide until the layer of metal beneath
is reached. AlKimia company monitors the thickness of the silicon oxide layer because thicker
layers require longer etching times.
a. A recent random sample of four wafers yielded a sample mean of 1.134 microns and a
standard deviation of 0.06. Construct a 95% confidence interval for the true mean
thickness
b. Explain in words the meaning of the 95% confidence interval obtained in (a) given the
above context
c. Find the sample size required to estimate the true mean thickness to within +0.01
micron using a 95% confidence interval.
4.
[Bonus 5 pts] The yields from an ethanol-water distillation column have a standard deviation of 1%.
A random sample of eight recent batches produced these yields and summary statistics.
.
0.90
0.90
Mean = 0.9075
0.93
0.87
0.95
0.93
0.86
0.92
Standard Deviation = 0.03105
a. Construct a 99% confidence interval for the true mean yield
b. Explain in words the meaning of the 99% confidence interval you obtained in (a) given
c.
the question context
Find the sample size required to estimate the true mean yield to within +0.5% using a
99% confidence interval.
ID number:____________________________
You must show all work to receive full credit
Name:______________________
ID number:____________________________
You must show all work to receive full credit
Name:______________________