Computer Assignment 2
Solve the following problems using Minitab to do the calculations.
Your computer output for this part should be your first page..
A. Suppose that 8% of all steel shafts produced by a certain process are
nonconforming but can he reworked (rather than having to be scrapped).
Consider a random sample of 1000 shafts and let X denote the number
among these that are nonconforming and can be reworked.
(1) Find the exact probability that X is
between 75 and 90 inclusive.
(2) Do the problem again this time using the normal approximation to
the binomial distribution using the continuity correction
(3) Do the problem again this time using the normal approximation to the
binomial distribution without the continuity correction.
Which of (2) and (3) give a better approximation to the exact value?
B. Suppose that only .1% of all computers of a certain type experience
CPU failure during the warranty period. Consider a sample of 300,000
computers.
(1) What is the expected value and standard deviation of the number of
computers in the sample that fail during the warranty period? (Do this
part by hand.)
(2) Using an appropriate binomial distribution find the probability that at
most 308 sampled computers fail during the warranty period?
(3) Using an appropriate Poisson distribution approximate the probability
at most 308 sampled computers fail during the warranty period?
(4) Use the normal approximation to the binomial distribution with the
continuity correction to approximate the probability that at most 308
sampled computers fail during the warranty period?
(5) Which approximation is more accurate?
2. Use Minitab to do this problem that demonstrates The Central Limit
Theorem
Do the computations in part A and answer the questions on page 2
stapled to the front of the computer output that should follow.
A.This part is to be done by hand. You will use a exponential distribution
with mean a where a is the number of letters in your last name. Thus, if
you have 20 letters in your last name you will use
1f(x)e,0x20−=<
x/20
For your value of the parameter a find the mean and the standard
deviation of the distribution by evaluating appropriate integrals. It
will not suffice to substitute in the formulas below.
For
your value of a you should get an answer with numerical value.
()Exa,sd(X)a==
You will now simulate your distribution 100 times.
calc>randomdata>exponential
In dialog box
Generate 100 rows of data
Store in columns c1-c100
Scale your value of a
Threshold 0
OK
enter the commands
rmeans c1-c100 c101
Make a stem and leaf display for c50 using the pull down menu or the
command
stem-and-leaf c50
describe c50
Make a stem and leaf display for c101 using the pull down menu or the
command
stem-and-leaf c101
describe c101
Make normal probability plots for c50 and c101.
MTB
Answer the following questions on the sheet stapled to the front of your
computer output.
1. Based on the stem and leaf display and the normal probability plot for
c50 does the data appear to be normally distributed? Explain your
answer.
2. Answer the same question for c101.
3. What is the mean and the standard deviation obtained in the describe
command for c50 and c101?
4. What should the mean and standard deviation be in theory for c50? for
c 101?[Hint for c50 it should be what you got by integration in part A.
For c101 the mean is the same and the standard deviation is divided by
10]
5. Compare the mean and standard Deviation in questions 3 and 4 by
finding the percentage error?
6. State the Central Limit Theorem carefully and explain how the results
you obtain in c101 validate it for your problem.
The solution will be different for students who work
independently but the conclusions should be similar. If
you get a large percentage error for your mean and/or
standard deviation check your calculation of the
theoretical mean and standard deviation. Chances are
pretty good that you made a mistake.