## Mathematics 210 - Spring term 2005 - Eighth assignment

This assignment is concerned with probability distributions. It is due before class time Wednesday, March 30.
• 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?

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• 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.

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• 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.

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• Question 4. Same question, but now for a loaded coin with the probability of heads equal to 0.43.

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• 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 105. Put those numbers in 10 bins (by their digit in the first place they might be non-zero) 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?)

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If you find these questions confusing, please write me.