222 Fundamentals of Statistics
that the average horizontal location of
her or his shots was within 0.2 unit of
the bull’s eye?
d. How many shots would a shooter
with the highest accuracy have to take
before achieving similar confi dence
in the average placement of his or her
shots?- Study the properties of the Poisson dis-
tribution by doing the following:
a. Open a blank workbook and, using
the Create Random Data command
from StatPlus, create 16 columns of
100 rows of Poisson random values
with l 5 0.25.
b. Create another column in your work-
book containing the average values
from those columns.
c. Create a histogram of the fi rst col-
umn of random Poisson values with
a superimposed normal curve.
Create a second histogram of the
column averages with a superim-
posed normal curve. Compare the
two curves.
d. Calculate the average and standard
deviation of the two columns.
e. How do these calculated values com-
pare to the value of l? See Exercise 7
for more information on the Poisson
distribution.
f. Save your workbook as Poisson
Distribution Analysis to the Chapter05
folder. - Repeat questions a. through d. of
Exercise 16 with 16 columns of 100
rows of binomial random values where
the number of trials is 16 and the value
of p is .25. How do the averages in part d
compare with the value p 5 .25? What
about the standard deviations computed
in part d? Save your workbook as
Binomial Distribution Analysis to the
Chapter05 folder.
1 8. Repeat questions a. through d. of Exer-
cise 16 with 16 columns of 100 rows
of Bernoulli random values where
p 5 .25. How do the averages in part d
compare with the value p 5 .25? What
about the standard deviations com-
puted in part d? Save your workbook as
Bernoulli Distribution Analysis to the
Chapter05 folder.- Repeat questions a. through d. of Exer-
cise 16 with 16 columns of 100 rows of
uniform random values where the lower
boundary is 0 and the upper boundary
is 100. Save the workbook as Uniform
Distribution Analysis to the Chapter05
folder. - True or false: According to the Central
Limit Theorem, as the size of the sample
increases, the distribution of the obser-
vations approximates a normal distribu-
tion. Defend your answer. - You want to collect a sample of values
from a uniform distribution where m is
unknown but s 5 10.
a. How large a sample would you need
to estimate the value of m within
2 units with a confi dence level of
95%?
b. How large a sample would you need
to estimate the value of m within
2 units with a confi dence level of 99%?
c. If the sample size is 25 and m is 50,
what is the probability that the sam-
ple average will have a value of 48
or less? - At the 1996 Summer Olympic games in
Atlanta, Linford Christie of Great Britain
was disqualifi ed from the fi nals of the
men’s 100-meter race because of a false
start. Christie did not react before the
starting gun sounded, but he did react in
less than 0.1 second.