1. A single toss of a fair coin results in either 0 or I head, each with probability 1/2. Define H= number of heads obtained on a single toss. The mean of His #,, = 0.5 and the standard deviation of His o,, = 0.5. Suppose you toss a fair coin four times. Define 7 = total number of heads obtained. Find the mean and standard deviation of T. 2. The time X it takes Professor Sawyer to drive to campus on a randomly selected day follows a distribution that is approximately Normal with mean 37 minutes and standard deviation 3 minutes. After parking his car it takes an additional 3 minutes to walk to his classroom and 2 minutes to start the computer. Then he is ready to begin class. Let T= the total time it takes Professor Sawyer to get to his classroom and be ready to begin class. Describe the shape, center, and variability of the probability distribution of T. 3. Six percent of the computer chips produced by Cheapo Chips are defective. Each month a random sample of 200 chips manufactured in that month is selected. Let X = the number of defective chips in the sample. (a) Calculate the mean and standard deviation of X. (b) Find the probability that 8 or fewer chips in a sample of 200 are defective. (c) To reduce the percentage of defective chips, the company contracts with a new supplier for some important components. In the next month, the sample of 200 chips has only 8 defective ones. Can the company conclude that the new components have reduced the rate of defective chips produced? Explain