Mathematics 210  Spring term 2005  Eighth assignment
This assignment is concerned with probability distributions.
It is due before class time Wednesday, March 30.

Go to the MathSheet home page
and then to the new applet page. Open a running
copy of the spreadsheet and return to this page.

Log in immediately: File/Log in. Your login id is your
Mathematics Department login name, and your password
is your student number. This allows you to save
and load spreadsheet files.
Save your work frequently.
To put it in simpler terms,
save your work frequently.

Question 1.
Make a table of areas under the graph
of the standard normal function, spaced at intervals of 0.01
from x=0 to 5. Use Simpson's rule.
How accurate are the values for x=1, 2, 3, 4, 5?
Save as m210.8.1.ms.

Question 2.
Use linear interpolation and interpolation using Simpson's rule
to find the area under the standard normal curve between x=0 and 1.27568.
Save as m210.8.2.ms.

Question 3.
Find the exact probability and that obtained by using the
normal approximation for obtaining between 80 and 123 heads in a toss of 200 fair coins.
Save as m210.8.3.ms.

Question 4.
Same question, but now for a loaded coin with the probability of heads equal to
0.43.
Save as m210.8.4.ms.

Question 5.
Set up 500 random numbers in column a
(with rand). In some
column b
set up those same numbers rounded to 5 decimal places,
and in column c the differences, scaled up by 10^{5}.
Put those numbers in 10 bins (by their digit in the
first place they might be nonzero)
and make a bar graph of the distribution.
(You will have to use other columns as well. rand returns a random value.
Convert them when you have them. At some point you'll have to sort things.
How will you get the rounded values?)
Save as m210.8.5.ms.
If you find these questions confusing, please
write me.
