Assignment

1. A company that manufactures large LCD screens knows that not all pixels on their screen light, even if they spend great care when making them. In a sheet 8ft by 10 ft that will be cut into smaller screens, they find an average of 4.4 blank pixels. They believe that the occurrence of blank pixels are independent. Their warranty policy states that they will replace any screen sold that shows more than 2 blank pixels. Complete parts a through d below.

a) What is the mean number of blank pixels per square foot?
b) What is the standard deviation of blank pixels per square foot?
c) What is the probability that a 2 ft by 3 ft screen will have at least one defect?
d) What is the probability that a 2 ft by 3 ft screen will be replaced because it has too many defect?

2. An insurance company estimates that it should make an annual profit of $220 on each homeowner's policy written, with a standard deviation of $7000. Complete parts a through e.

a) Why is the standard deviation so large? CHOOSE ONE

• The insurance company will either make a very large amount of money on a policy or lose a large amount of money for a claim, which results in a small mean, but also in a large standard deviation

• There will be many gains of $220 with a few large losses

• The standard deviation is large because it is found using squared values

• Claims range in size so the amount of damage they will have a large standard deviation

b) If the company writes only two of these policies, what are the mean and standard deviation of the annual profit?

c) If the company writes 10,000 of these policies, what are the mean and standard deviation of the annual profit?

d) Do you think the company is likely to be profitable? CHOOSE ONE

• No. catastrophes are far too unpredictable to expect a profit
• Yes. The expected value is greater than zero
• No. the variance is larger than the mean
• Yes. $0 is 3.1 standard deviation below the mean for 10,000 policies

e) What assumptions underlie your analysis? CHOOSE ONE

• Losses are dependent
• The annual profit on a policy is a discrete random variable
• The annual profit is a continuous random variable
• Losses are independent of each other

Can you think of circumstances under which those assumptions might be violated?

• A major catastrophe with many policies in an area
• Charges for repairs are only calculated in terms of whole dollars
• A new coin is created that represent a half cent
• In the country, houses are very far apart from each other

3. given the independent random variables with the means and standard deviations are shown, find the mean and standard deviation of each of these variables:

a) 4.4X
b) 3Y - 62
c) 2X + 4Y
d) 3X - 4Y
e) Y1 + Y2