Forum
M8 L1
First post
First response
Answer the questions given, then explain how you obtained your
answers. Post your answers to the Forum. After you make your post
you'll be able to see others' answers.
You can post your answers by clicking on "Reply" below. After you
make your post you'll be able to see others' answers. Check back
periodically to see who else has posted. Make comments on the
correctness or errors to answers given by two other classmates.
1. You have a binomial situation B(50, 0.5).
a) Find P(X = 25)
b) How would your answer to part a change if n is smaller? Explain
c) How would your answer to part a change if n is larger? Explain
2. For each of the following, given n and p, find the probabilities
indicated.
Assume the setting is binomial
a) n = 40, p = 0.4, P(X ≤ 12)
b) n = 20, p = 0.2, P(X > 8)
c) If you could only have one of the options binompdf or binomcdf
available
on your calculator, which would you choose and why?
3. Women make up about 45% of the labor force. You take a sample of
20
workers and are interested in the number of females.
a) Is this a binomial setting? Why
b) From 20 randomly selected workers, what is the probability that
exactly 6
will be women?
c) What is the probability that at most 6 will be women?
d) What is the probability that at least 6 will be women? How does
this
question differ from 7c?
e) How many women would you expect in this random sample?
f) How would you design and run a simulation to answer question
7e?
Run it and compare your answers?
You have a binomial situation B(50, 0.5).
a) Find P(X = 25) 0.1122
b) How would your answer to part a change if n is smaller?
Explain
The probability would be smaller. For example, if n = 40, then
P(X = 25) = 0.0366
c) How would your answer to part a change if n is larger? Explain
The probability would still be smaller. For example, if n = 60, then
P(X = 25) = 0.0450
2. For each of the following, given n and p, find the probabilities
indicated.
Assume the setting is binomial
a) n = 40, p = 0.4, P(X ≤ 12) binomcdf(40, 0.4, 12) = 0.1285
b) n = 20, p = 0.2, P(X > 8) 1 - binomcdf(20, 0.2, 8 = 0.00998
c) If you could only have one of the options binompdf or
binomcdf available
on your calculator, which would you choose and why?
Answers vary according to student preferences
3. Women make up about 45% of the labor force. You take a sample
of 20
workers and are interested in the number of females.
a)
Is this a binomial setting? Why
Yes, it is binomial because
 Each observation is success (worker is female) or failure
(worker is not female)
 The probability of success for each observation is the
same (0.45)
 There are a fixed number of observations (n = 200)
 Each observation is independent
b) From 20 randomly selected workers, what is the probability
that exactly 6
will be women?
P(X = 6) = binompdf(20, 0.45, 6) = 0.1244
c)
What is the probability that at most 6 will be women?
P(X ≤ 6) = binomcdf(20, 0.45, 6) = 0.1299
d) What is the probability that at least 6 will be women? How
does this
question differ from 7c?
P(X ≥ 6) = 1 – binomcdf(20, 0.45, 5) = 0.9947
e)
How many women would you expect in this random sample?
The expected value is the same as the mean of the distribution
np = 20(0.45) = 9
f) How would you design and run a simulation to answer
question 7e?
Run it and compare your answers?
One way could be to use a random number table and assign the
numbers 00 – 44 to be “success” and 45 – 99 to be “failure”. Read
two digits, 20 times and record the number of “successes”. Do this
multiple times (say, 10 times) and get an average of successes out
of 10 trials.
M9 L1
Samplin
g
Distribu
tions
In your post, answer the following questions. After you make your
post you'll be able to see others' answers.
TPOS 2nd edition:
Work problems 9.1, 9.2, 9.3, 9.4, 9.5.
TPOS 3rd edition:
Work problems 9.1, 9.2, 9.3
TPOS 2nd Edition
9.1 answers are in back of book
9.2 p-hat = 7.2% is a statistic.
9.3 answers are in back of book
9.4 Both x-bar = 335 and x-bar = 289 are statistics.
9.5 answers will vary
TPOS 3rd Edition
9.1 answers are in back of book
9.2
a) p-hat = 48% is a statistic. p-hat = 52% is a
parameter.
b) x-bar = 335 and x-bar = 289 are both statistics.
9.3 answers are in back of book
M9 L1
Before you post (see below), use your calculator to answer the
following questions:
1. Answers will vary, one solution is given:
samplin
g
distribu
tions
part 2
1. The Bureau of Labor Statistics reports that 25% of
people with full-time jobs spend 49 hours or more on
the job per week. In a random sample of 20 people with
full-time jobs, how many people would be likely to
spend 49 or more hours on the job?
a) Use randbin to design and run a simulation to
answer the question. Run the simulation 100 times.
a) b) c) 96% d) 96 people
e) The answers are the same.
2. Answers will vary, one solution is given:
b) Find the mean and standard deviation of your
sampling distribution for the number of people in a
sample who spend more than 49 hours per week
working.
a) b) 96% c)
c) Determine the percent of the trials that are within two
standard deviations of the mean.
d)95.45 and 96% are pretty close! There is only .55%
difference
3. RandInt(1,18,20) will produce 20 integers between
1 and 18. RandBin(100,.18,20) will produce the
results of 20 binomila experiments with n=100 and
p=.18.
d) How many people who work full time are likely to
spend 49 or more hours on the job each week? (Note:
this is where you find the 5th and 95th percentile - like
you were shown in the PowerPoint)
e) Compare the results in parts (c) and (d).
2. The Marriott Corporation states that about 70% of
extended stay travelers (people who stay more than
one night at a motel) were under 45 years of age. If a
random sample of 20 extended stay travelers is taken
at a given hotel, is it likely that there are 17 under 45
years of age?
a) Use randBin to design and run a simulation to
answer the question. Run the simulation 100 times.
b) In a sample of 20, how many extended stay travelers
are likely to be under 45 years of age? (Note: this is
where you find the 5th and 95th percentile - like you
were shown in the PowerPoint)c) What is the
theoretical mean and standard deviation of the number
of extended stay travelers that are under 45 years of
age in a random sample of 20 travelers?
d) Use answers to part (c) with normalcdf to estimate
the percentage of the trials within two standard
deviations of the mean. How does this compare with
your answer for part (b)?
3. What is the difference between randInt(1,18,20)
and randBin(20,.18,100)?
Now click "Reply" and post your answers to questions 1b, 2b, and 3.
After you make your post you'll be able to see others' answers.
M9 L1
Samplin
g
distribu
tions
part 3
Before you post (see below), answer the following questions
TPOS 2nd edition:
Work problems 9.8, 9.10, 9.11, 9.15.
TPOS 3rd edition:
Work on problems 9.8, 9.9, 9.10, 9.15
Now click "Reply" and post your answer to question 9.10. After you
TPOS 2nd Edition:
9.8 (a).
count
9
.045
1
make your post you'll be able to see others' answers.
13
.065
3
14
.070
2
15
.075
5
16
.080
11
17
.085
12
18
.090
12
19
.095
9
20
.100
7
21
.105
5
22
.110
6
23
.115
7
24
.120
10
25
.125
4
26
.130
1
27
.135
2
28
.140
2
30
.150
1
(b) the histogram has a very rough mound
shape. The sampling distribution is normal,
although this sample of 100 does not strongly
suggest it.
(c) .0981 the bias seems to be small.
(d ) The mean of the sampling distribution should
be p=.10.
(e) The mean would still be .1, but the spread would
be smaller.
9.10(a) large bias ,large variability
(b) small bias ,small variability
(c) small bias ,large variability
(d) large bias ,small variability
9.11 answers are in back of book
9.15 answers are in back of book
TPOS 3rd Edition
9.8 Same answers as #9.8 above, TPOS 2nd Edition
9.9 answers are in back of book
9.10 – Same as 9.10 above
9.15 answers are in back of book
M9 L1
Penny
samplin
g
In this assignment you will complete Activity 9B
from pages 520-521 (TPOS 2nd edition) or pages
596-597 (TPOS 3rd edition), except you will use a
computer simulation instead of actual pennies to
complete this exercise of sampling pennies.
Go to
the http://statweb.calpoly.edu/chance/applets/SampleD
ata/SampleData.html site and simulate sampling
pennies. Follow the general outline from Activity 9B, but
allow your sample sizes and numbers to go larger, as
time of counting and recording the pennies is not a
limitation. Observe and record the sample means for
each different sample size.
After your pennies simulation, reply to this post and
include:
1. A short summary of your sampling distributions for
different sample sizes. What trends or patterns do you
notice in the sampling distributions?
2. What major statistical principle or idea is
illustrated in the Sampling Pennies exercise? Can
you explain why this principle might be so useful in
practicing statistics?
3. A summary of what you have learned from this
exercise.
4. One question you still have about sampling
distributions.
M9 L2
Samplin
g
Distribu
tions
with
proporti
ons
In your post, answer the following questions. After
you make your post you'll be able to see others'
answers.
TPOS 2nd edition:
Work problems 9.36, 9.39.
TPOS 3rd edition:
Work problems 9.36, 9.41
TPOS 2nd Edition
9.36 The mean return x-bar is approximately Normal, with mean μxbar= 13.2% and a standard deviation σx-bar=
(17.5)/(√40)=2.7670%. Therefore, P(x-bar > 15%) = P(Z > 0.65) =
0.2578, and P(x-bar < 10%) = P(Z < -1.16) = 0.1230.
9.39 answers are in back of book
TPOS 3rd Edition
9.36 answer same as #9.36 above, TPOS 2nd Edition
9.41 answers are in back of book