Allied MAT130 module 4 homework

PART
I: SHORT RESPONSE

Directions: Please answer each of the following questions thoroughly.

1. What requirements are
necessary for a normal probability distribution to be a standard normal
probability distribution?

2. What is the difference
between a standard normal distribution and a nonstandard normal distribution?

3. Find the indicated
values for the following problems:
a.
z0.05
b.
z­0.01
c.
z0.10­
d.
z0.02

4. Based on data from the
National Health Survey, men’s heights are normally distributed with mean 69.0
in. and standard deviation 2.8 in, whereas women’s heights are normally
distributed with mean 63.6 in. and standard deviation 2.5 in. The Gulfstream
100 is an executive jet that seats six, and it has a doorway height of 51.6 in.
Use this information to answer the following problems:
a.
What percentage of adult men
can fit through the door without bending?
b.
What percentage of adult women
can fit through the door without bending?
c.
Does the door design with a
height of 51.6 in. appear to be adequate? Why didn’t the engineers design a
larger door?
d.
What doorway height would allow
60% of men to fit without bending?

5. What is the standard
error of the mean?

6. Assume that SAT scores
are normally distributed with mean ? = 1518 and standard deviation ? = 325. Use
the Central Limit Theorem to answer the following:
a.
If 1 SAT score is randomly
selected, find the probability that it is greater than 1600.
b.
If 64 SAT scores are randomly
selected, find the probability that they have a mean greater than 1600.

7. Assume that a sample is
used to estimate a population proportion p. Find the margin of error E that
corresponds to the given statistics and confidence level.
a.
n = 500, x = 220, 99%
confidence
b.
90% confidence; the sample size
is 1780, of which 35% are successes

8. Use the given sample
data and confidence level to construct the confidence interval estimate of the
population proportion p for each problem.
a.
n = 2000, x = 400, 95%
confidence
b.
n = 5200, x = 4821, 99%
confidence

9. A design engineer for
the Ford Motor Company must estimate the mean leg length of all adults. She obtains a list of the 1275 employees at
her facility, then obtains a simple random sample of 50 employees. If she uses this sample to construct a 95%
confidence interval to estimate the mean leg length for the population of all
adults, will her estimate be good? Why
or why not?

10. A simple random sample
of 40 salaries of NCAA football coaches has a mean of $415,953 and a standard
deviation of $463,364.
a.
Find the best point estimate of
the mean salary of all NCAA football coaches.
b.
Construct a 95% confidence
interval estimate of the mean salary of an NCAA football coach.
c.
Does the confidence interval
contain the actual population mean of $474,477?

11. Use the given confidence
level and sample data below to find (a) the margin of error and (b) the
confidence interval for the population mean. Assume that the sample is a simple random
sample and the population has a normal distribution. 99% confidence; n = 7,.png”>= 0.12 , s = 0.04

12. What is an unbiased
estimator? Is the sample variance an
unbiased estimator of the population variance?
Is the sample standard deviation an unbiased estimator of the population
standard deviation?

13. Use the given confidence
level and sample data to find a confidence interval for the population standard
deviation. In each case, assume that a simple random sample has been selected
from a population that has a normal distribution. 95% confidence; n = 25,.png”>= 81.0, s = 2.3

14. Twelve different video
games showing substance use were observed and the duration times of game play
(in seconds) are listed below (based on data from “Content and Ratings of
Teen-Rated Video Games,” by Haninger and Thompson, Journal of the American
Medical Association, Vol. 291, No. 7). The design of the study justifies the
assumption that the sample can be treated as a simple random sample. 4049 3884 3859 4027 4318 4813 4657 4033 5004
4823 4334 4317
a.
Use the sample data to
construct a 95% confidence interval estimate of ?, the mean duration of game
play.
b.
Use the sample data to
construct a 99% confidence interval estimate of ?, the standard deviation of
the duration times of game play.

PART
II: PROJECT

For
this Module 4 Homework Assignment, please submit your response to the
following:

Document your
progress. Who did you interview? How many people did you interview? If you collected data, please submit it
below. If not, please explain what you
did to contribute to this assignment this past week.

Directions: This assignment is a course-long project whereby you will work on
the project in each module. You will
turn in your completed project at the end of Module 8.

Create a survey question to ask others. The
following are examples or some survey questions:

1.
Choose a random number between
1 and 10 inclusive.
2.
What month of the year does
your birthday fall on? Write the numeric
value from 1 to 12.
3.
How many keys are in your
possession at this time?
4.
How many siblings do you have?

In Module 1, you will submit your survey question
to your instructor for approval. Once
you are notified of its approval, you may begin conducting a survey using your
question.

You will need at least 25 participants and
will need to keep the following record for each person:

a.
Gender
b.
Age
c.
Date surveyed
d.
Survey response

Please also keep a count, if any, non-willing
participants. For example, if you chose
the first survey question, then you might have the following records:

Participant #

Gender

Age

Date Surveyed

Survey Response

1

M

18

12/10/12

5

2

F

42

12/15/12

8

3

M

34

12/17/12

1

In the Module 8 Homework Assignment, you will
be asked to analyze your survey results, so please be sure to begin conducting
your survey as soon as your question is approved. Try getting 5 participants a week to satisfy
the required number of participants.