## Mathematics 210 - Spring term 2005 - Ninth assignment

This assignment is concerned with probability distributions, mostly approximation by the normal. It is due before class time Monday, April 5.
• Question 1. In this question you want to simulate tossing 5 coins 100 times. Place in some carefully thought out way 500 random numbers on a spreadsheet, in groups of 5. Convert these to constants. Then in another 500 cells record these as 0 or 1. Add up the score in each group, sort the scores, and make a bar graph of the count of groups with scores of 0 to 5.

Save as m210.9.1.ms.

• Question 2. Read the notes on areas under the wings of the normal function. Use the technique explained there to give the integral from 0 to 5.13 of the standard normal function, as accurately as you can.

Save as m210.9.2.ms.

• Question 3. Load your table of areas under the normal curve from the last assignment, or make a new one, in steps of size 0.01 from 0 to 5. Use it if necessary to answer this question: If you toss a single die 100 times, what is the probability of getting between a total score of bewteen 300 and 400? Less than or equal to 250?

Save as m210.9.3.ms.

• Question 4. If you choose 500 numbers at random from the interval [0,1] and then add them together, what is the probability of getting a total sum of 300 or more?

Save as m210.9.4.ms.

If you find these questions confusing, please write me.