1.

You are told that P(A) = 0.5, P(B) = 0.4, and the events A, B are independent.

What is the value of P(A and B)?

Please give your answer correctly rounded to two decimal places, NOT as a percentage.

(If you give your answer as a percentage, it will be MARKED AS WRONG)

2.

You are told that P(A) = 0.4, P(B) = 0.4 and P(A or B) = 0.68

What is the value of P(A and B)? Give you answer to two decimal places.

3.

A researcher wants to examine the relationship between opinion of a proposed new gas mine and the political party followed. The observed frequencies are summarized in the following table.

	Opinion
For	Against	Undecided
Political party followed	Greens	27	23	20
Labor	3	4	28
Liberal	10	30	25

What is the total number of respondents in this survey?

4.

Sales in a caf are approximately normally distributed with a mean of $12 and a standard deviation of $4. What is the probability that one randomly selected sale is less than $15?

0.22660.77340.7500-0.75001.0000

5.

Suppose that a random variable X is normally distributed with standard deviation 0.6, however the mean is unknown. It is known that 2.5% of values are below an x value of 15. What is the value of the mean? Give your answer to two decimal places. Do NOT include units in your answer.