Homework 3, Math 320, Spring 2001

Name:____________________________      Section number:______

## Math 320 Homework #3 --- Due 2/9

Include your name, section number, and homework number on every page that you hand in. Enter ``Section 1'' for the morning class (10-11AM) and ``Section 2'' for Professor Sawyer's class (12-1PM).

You can begin the exposition of your work on this page. If more room is needed, continue on sheets of paper of exactly the same size (8.5 x 11 inches), lined or not as you wish, but not torn from a spiral notebook. You should do your initial work and calculations on a separate sheet of paper before you write up the results to hand in.

Output from Excel must have your name, Section number, and the homework number in cell A1. Staple all sheets together. No unstapled papers will be accepted.

1.  A survey of the choices of medical plans used by employees of the Acme Widget factory yielded the following results:

Plan Single Married Total
1 60 20 80
2 30 120 150
3 35 75 110
Total 125 215 340

Answer the questions in Exercise 4.78 on page 161 in the text, using the Acme Widget data instead of the data in that exercise. Show your calculations.

2.  This problem consists of Exercises 4.38-4.41 on pages 156-157.  If you know the number of games played in each of the World Series of 1992-1997, then you are welcome to include that in the data as well.

(i) #4.38 p. 156. Construct a probability model (that is, find the probability density function) for the number of games played and use it to find the population mean.
(ii) #4.39 p. 157. Graph the cumulative distribution function (c.d.f.).
(iii) #4.40 p. 157. Find the population standard deviation.
(iv) #4.41 p. 157. Find the population median and interquartile range.

3.  This exercise is based on #4.24 on page 146.

(i) Do #4.24 on page 146.
(ii) What is the probability that a randomly selected tire has less than 1/8 inch of tread on it?
(iii) (See #4.26 on page 146). Find the cumulative distribution function and graph it.
(iv) Use the (cumulative) distribution function to find the probability that a randomly selected tire has between 1/8 and 3/8 of an inch of tread.

4.  Do parts (a)-(d) of Exercise #4.62 on page 159. (Hint: Construct a contingency table.)

5.  Do parts (a)-(b)-(c)-(d)-(e) and (g)-(h) of Exercise #5.1 on page 176. Do not use Table A1. (The parameters p are not in the table.) However, you can use a calculator or Excel. (See the Excel/Calculator notes for hints about using a TI-83 calculator or Excel to find binomial probabilities.)