# Mid Term Exam - DOC

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```					MA 211 – Final Exam                                                Name:     Craig S Adams

Rules: Open book and notes. You may not discuss any aspect of this exam with anyone
other than the instructor. You must submit your answers either electronically or in hard copy
no later than 5 pm, 8 Mar 2002. Direct answers are acceptable. However, any supporting
material (i.e. showing your work) will increase the probability of “partial credit” given an
incorrect response. Indicate your final answer by drawing a square around it.

1) Cruise ships of the Royal Viking line report that 80 percent of their rooms are
occupied during September. For a cruise ship having 800 rooms, what is the
probability that 665 or more are occupied in September? How do you think one
could use this type of information to the company’s advantage?

Mean: 800(.80)=640
Variance: 880(.80)(.20)
Std Dev: 11.31

z=X-mean/std dev
Correction Factor [case 1]
z=664.5-640/11.31
z=2.166
P(x = to or grater than 665)=.015

2) It is estimated that 10 percent of those students taking the statistics portion of the
GRE fail that section. Sixty students are taking the exam next week.
a) How many would you expect to fail? What is the standard deviation?

Mean: 60(.10)= 6

Variance: 60(.10)(.90)=5.4

Std Dev: 2.32

b) What is the probability the exactly two students will fail?

p(x)=nCxx(1-)n-x , n=60, x=2, =.10

p(2)= .0393

Reference Attachment #1

c) What is the probability that at least two students will fail?

p(x is at least 2) = 1-[p(x=2) – p(x less than or =2)]

p=.9862

Reference Attachment #1

MA211 (Final Exam) -- 1 of 5
MA 211 – Final Exam                                            Name:     Craig S Adams

3) An Air Force study indicates that the probability of a disaster such as the January
28, 1986, explosion of the space shuttle Challenger was 1 in 35. The Challenger
flight was the 25th mission of the year.
a) How many disasters would you expect in the first 25 flights?

P= 1/35
P= .0286
Variance= 35(.0286)(.9714)=.9724
Std Dev= .986
Z=25-35/.986=10.14
Z area=.499999999999999999999999
Zero

b) Use the normal approximation to estimate the probability of at least one
disaster in 25 missions.

No! n 5
The normal probability distribution is a good approximation to the
binomial when n and n(1-) are both at least 5.
n=25,  =.0286, n =.715, n(1-)=24.285

c) Considering the number of missions per year, and the risks associated
with failure, do you think that these qualify as “acceptable risks?”

Yes

4) At the downtown office of First National Bank, there are five tellers. Last week, the
tellers made the following number of errors each: 2, 3, 5, 3, and 5.
a) How many different samples of 2 tellers are possible?

10 Referance Attachment #3

b) List all possible samples of size 2 and compute the mean of each.

Reference Attachment #3

c) Compute the mean of the sample means and compare it to the
population mean.

Population mean = 3.6
Mean of the sample mean = 3.6
No difference between the population mean and the mean of the sample
mean.

MA211 (Final Exam) -- 2 of 5
MA 211 – Final Exam                                          Name:     Craig S Adams

5) A recording company wants the mean lengths of the “cuts” on a CD to be 135
seconds (2min, 35 sec). This will allow the disk jockeys to have plenty of time for
commercials within each 10-minute segment. Assume the distribution of the length
of the cuts follows the normal distribution with a standard deviation of 8 seconds.
Suppose we select a sample of 16 cuts from various CDs sold by the producer.
a) What can we say about the shape of the distribution of the sample
mean?

Normal distribution: Bell shaped, Symmetric, and Asymptotic.

b) What percentage of the sample means will be greater than 140 minutes?

.0062 Reference Attachment #4

c) What percentage of the sample means will be greater than 128 minutes?

.9998 Reference Attachment #4

d) What percentage of the sample means will be greater than 128 but less
than 140 minutes?

.9936 Reference Attachment #4

6) You need to estimate the mean number of travel days per year for your company’s
aircrew. You identified a previous study that was comparable to your problem at
hand. The study data had a mean of 150 days and a standard deviation of 14 days.
If you must estimate the mean of the population within 2 days (of error), how many
aircrew should you sample? Use the 90% confidence level.

n=(z*s/E)2 , z90 = 1.65, s=14, E=2
n=[(1.65*14)/2)2

n=133

7) Past surveys reveal that 30% of tourists going to Las Vegas to gamble during a
weekend spend more that \$1,000. Management wants to update this percentage.
a) The new study is to use the 90% level. The estimate is to be within 1%
of the population proportion. What is the necessary sample size?

n=p(1-p)(z/E)2, z90 =1.65, p=.30, E=.01

n=5682

MA211 (Final Exam) -- 3 of 5
MA 211 – Final Exam                                           Name:    Craig S Adams

b) Management said the sample size determined in part (b) is too large.
What can be done to reduce the sample? Based on your suggestion,
recalculate the sample size.

Change the estimate to be within 10% of the population proportion.
n=p(1-p)(z/E)2, z90 =1.65, p=.30, E=.10

n=57

8) The policy of the LA Transit Authority is to add a bus route if more than 55% of the
potential commuters indicate they would use the particular route. A sample of 70
commuters revealed that 42 would use a proposed route from LAX to the downtown
area. Does the LAX-Downtown route meet the LATA criterion? Use the 0.05
significance level.

Yes. Accept the H0. Reference Attachment #5

Single tail. Population proportion.

9) The Human Relations Department of Acme, Inc. would like to include a dental plan
as part of the benefits package. The question is: How much does a typical
employee and his or her family spend per year on dental expenses? A sample of 45
employees reveals the mean amount spent last year was \$1,820, with a standard
deviation of \$660.
a) Construct 95% confidence interval for the population mean

CI= x(bar) + or – z*s/sqrt of n
CI= 1820 + or – 1.96(660/sqrt of 45)

CI = 1627 to 2012 Reference Attachment #6

b) The information from part (a) was given to the president of Acme. She
indicated she could afford \$1,700 of dental expenses per employee. Is
it possible that the population mean could be \$1,700? Justify your

Yes. It is possible1700 is between the upper and lower confidence level,
but risky, Data suggests the population mean will be closer to 1800
because the sample size is large enough the sample mean should be an
accurate predictor of the population mean.

MA211 (Final Exam) -- 4 of 5
MA 211 – Final Exam                                                  Name:   Craig S Adams

10) A recent study by the American Automobile Dealers Association revealed the mean
amount of profit per car sold for a sample of 20 dealers was \$290, with a standard
deviation of \$125. Develop a 95% confidence interval for the population mean.

CI= x(bar) + or – t*s/sqrt of n
CI = 290 + or – 2.093/sqrt of 20

CI = 348 to 231 Reference Attachment #6

11) A recent article in the Wall Street Journal reported that the prime rate for large
banks now exceeds 9%. A sample of eight small banks in the Midwest revealed the
following prime rates (in percent)
10.1    9.3     9.2   10.2    9.3   9.6      9.4     8.8
-   At the 0.01 significance level, can we conclude that the prime rate for small
banks also exceeds 9%?

Two-tailed, because the question asks if the interest rates of the small banks is
equally(=) as high as the large banks.
Student’s t distribution because it is a small sample size.

Yes. Reference Attachment #7

-   Estimate the p-value.

P=.9984    Reference Attachment #7

Bonus Questions:

1) Find what you think will be a valuable Internet resource for future statistics
students. (Write down the URL and provide a brief description).

Don’t know.

2) If the homework was not a graded portion of this course, do you think students,
in general, would still try it to better comprehend the equations and their
application?

I think you need to have a set of graded problems every week. However, a quiz
or homework would have the desired results. To do both is a big workload.

MA211 (Final Exam) -- 5 of 5

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