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 6 ft by 10 ft (72 in. by 120 in.) that will be cut into smaller screens, they find an average of 4.7 blank pixels. They believe that the occurrences of blank pixels are independent. Their warranty policy states that they will replace any screen sold that shows more than 2 blank pixels.
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 defects?