Download Assignment #4

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STAT 307
Homework #4
Spring 2008
Due Monday 3/24/08
Note:
URI
- All questions should be handed in.
- Selected QUESTIONS would be graded.
1.
Find the area under the standard normal curve that lies to the right of
a. -1.07
2.
b. 1.56
d. 4.2
Determine the area under the standard normal curve that lies between
a. -2.18 and 1.44
c. 0.59 and 1.51
3.
c. 0
b. -2 and -1.5
d. 1.1 and 4.2
Find the area under the standard normal curve that lies
a. either to the left of -2.12 or to the right of 1.67
b. either to the left of 0.63 or to the right of 1.54.
4.
Obtain the following z-scores. (Choose closest value. If halfway, then
interpolate).
a. z0.20
b. z0.005
5.
In 1905, R. Pearl published the article “Biometrical Studies on Man. I.
Variation and Correlation in Brain Weight”. According to the study, brain
weights of Swedish men are normally distributed with a mean of 1.40
kg and a standard deviation of 0.11 kg. Obtain the percentage of
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Swedish men who have brain weights
a. between 1.5 kg and 1.70 kg.
b. less than 1.6 kg.
c. Determine the quartiles of the brain weights of Swedish men.
d. Obtain the 20th percentile of the brain weights of Swedish men.
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6.
Using the data in problem 5 above.
a. Determine the sampling distribution of the sample mean for samples
of size 3.
b. Repeat part (a) for samples of size 12.
c. Construct graphs for the original distribution and for the sampling
distributions for the mean brain weights for samples of size 3 and
12. Label the distribution accordingly. If you use Excel, then use
the mathematical formula for a normal random variable with
appropriate mean and standard deviation. A range of X values
from 1 to 2 in steps of 0.1 will suffice. Overlay all three curves
on the same graph.
d. Is it necessary to assume that brain weights of Swedish men are
normally distributed to answer parts (a) and (b)? Explain your
answer.
e. Determine the percentage of all samples of three Sweedish men that
have mean brain weights within 0.1 kgs of the population mean
brain weight of 1.40 kg.
f.
7.
Repeat part (e) for sample of size 12.
Some studies of Alzheimer’s disease (AD) have shown an increase in
CO2 production in patients with the disease. In one such study the
following CO2 values were obtained from 7 neocortical biopsy samples
from AD patients:
1009
1280
1180
1255
1547
2352
1080.
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(Could use Excel to answer parts (a) and (b) of the question. Work to
two decimal places.)
a. Find the normal scores associated with the observed sampled
values.
b. Find the Normal Probability Plot of the data above.
c. Comment on the normality of the data. Is there any hint of outliers in
the data? What about skewness? Explain.