Week 2/22

1. A small town has 5600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents’ responses, broken down by gender:

Men Women Total

In Favor 1400 280 1680

Opposed 840 3080 3920

Total 2240 3360 5600

A) What is the probability of a randomly selected resident being In Favor to the bridge?

B) What is the probability that a randomly selected resident is a Woman and is in Favor of the bridge?

C) What is the probability of a randomly selected resident being a Woman or in Favor of the bridge?

D) If a randomly selected resident is a Man, what is the probability that he is in Favor of the bridge?

E) Are gender and opinion about the bridge mutually exclusive events? Why?

F) Are gender and opinion about the bridge independent events? Why? Show some “proof” with probabilities.

2. How many Combinations of 3 students can be selected from a group of 10 students?

3. Describe the Sample Space for the experiment of selecting one resident from the total group in problem #1 above.

Week 3/1

1. The following probability distribution represents the number of people living in a Household (X), and the probability of occurrence (P(X)). Compute the Expected Value (mean), the Variance and the Standard Deviation for this random variable. Show Your Calculations for the Mean.

X 1 2 3 4 5

P(X) .19 .42 .29 .07 .03

2. Use the binomial formula to compute the probability of a student getting 7 correct answers on a 10 question Quiz, if the probability of answering any one question correctly is 0.71. SHOW YOUR WORK.

3. Submit your answers to the following binomial questions. You may use the appendix table B.1 to answer parts (a) and (b). According to a government study, 20% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:

a) what is the probability that 4 or more live in poverty?

b) what is the probability that 4 live in poverty?

c) what is the expected number (mean) that live in poverty? What is the variance? What is the standard deviation?