1. Let X define the random variable that is defined as the sum of two fair dice. Find the following probabilities. a. P{X=2} b. P{X=3} C. P{X=6} 2. Industry standards suggest that 25% of new vehicles require a service within the first year. Suppose 10 new vehicles were selected randomly. a. Is the selection of 10 vehicles a binomial experiment? Explain. b. What is the probability that none of the 10 vehicles will require a service? C. What is the probability that 4 out of 10 vehicles will require a service? d. What is the probability that at least 2 out of the 10 vehicles will require a service? 3. The amount of water in a 12-ounce can has a uniform distribution between 11.96 ounces and 12.05 ounces. a. What is the mean amount per can? b. What is the probability of selecting a can of water and finding it has less than 12 ounces? C. What is the probability of selecting a can of water and finding it has more than 11.98 ounces? d. What is the probability of selecting a can of water and finding it has more than 11.00 ounces? 4. According to a survey, women spent an average of 34 hours per week watching TV, and men, 29 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.5 hours and is 5.1 hours for the men. a. What percent of the women watch TV less than 40 hours per week? b. What percent of the men watch TV more than 25 hours per week? 5. Assume a binomial probability distribution with n=40 and p=0.55. Compute the following: a. The mean and standard deviation of the random variable. b. The probability that x is between 15 and 25, inclusive. (Hint: use the normal approximation to the binomial) 6. Waiting times to receive food after placing an order at the local sandwich shop follow an exponential distribution with a mean of 60 seconds. Calculate the probability a customer waits: a. Less than 30 seconds. b. More than 120 seconds. C. Between 45 and 75 seconds.