1.
x P(x)
0 0.15
1 0.25
2 0.1
3 0.5

Find the standard deviation of this probability distribution. Give your answer to 4 decimal places

2. Suppose that a box contains 8 cameras and that 4 of them are defective. A sample of 2 cameras is selected at random. Define the random variable x as the number of defective cameras in the sample.

Write the probability distribution for x

x P(x)

What is the expected value of x?

3. A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $450.

If they offer a 2 year extended warranty for $26, what is the company's expected profit or loss of each warranty sold? Round to the nearest cent.

$

4.
A bag contains 2 gold marbles, 8 silver marbles, and 27 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $6, if it is silver, you win $3. If it costs $1 to play, what is your expected profit or loss if you play this game?

5. A company estimates that 9% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $50.

If they want to offer a 2 year extended warranty, what price should they charge so that they'll break even (in other words, so the expected profit will be 0)