Homework 4, Math 320, Spring 2001

Name:____________________________      Section number:______

## Math 320 Homework #4 --- Due 2/16

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.

NOTE: Some of the following problems require values of P(X=x) or P(X<=x) for the binomial distribution. If these values are not on your Calculator and you do not have Microsoft Excel at your fingertips (click on those for more information), then you may be able to find the value in the back of the book. Table A1 has binomial cdf values for n<=20 and nine different values of p .

1. Do Exercise 5.12 on page 177.

2. A factory produces boxes of widgets with 20 widgets in a box. Whether or not the widgets are defective are independent events with probability 0.10 for each widget (that is, probability 0.10 that each widget is defective, independently of the others).

(i) What is the expected number of defective widgets in each box?
(ii) The sales department says that each box with 5 or more defective widgets results in an angry telephone call from a customer. What is the probability that a box of widgets has 5 or more defective widgets, resulting in an angry telephone call?
(iii) Suppose that widgets are shipped wholesale in cartons of 100 boxes of 20 widgets each, so that each carton contains 2000 widgets in 100 boxes. What is the expected number of angry telephone calls that results from each carton of widgets that is shipped?

3. Do Exercise 5.34 on page 202.  (Hint: What does a ``success'' mean in this context?)

4. Do Exercise 5.20 on page 191. Use either Tables A2 and A2* or else the statistical functions in Excel or a calculator.

5. Do Exercise 5.24 on page 191.

6. A person tosses a fair coin 1000 times. Use a normal approximation to find the probability that he or she obtains 535 or more heads. What is the Z-score for 535 heads in the normal approximation? (Assume that the number of heads obtained has a binomial distribution with n=1000 and p=1/2. Use the continuity correction for the normal or not, as you prefer.)

(Note: If your calculator can calculate this probability using a binomal distribution with n=1000 without crashing, then it may be using a normal approximation without telling you. Some older TI-83s crashed if you tried to use binomcdf( with n=1000 .)