1. Uniform: The amount of time, in minutes, that a person must wait for a bus is uniformly distributed between 0 and 15 minutes, inclusive. What is the probability that a person waits fewer than 12.5 minutes? What is the probability that will be between 0.5 standard deviation from the mean, 2. Slater customers are charged for the amount of salad they take. Sampling suggests that the amount of salad taken is uniformly distributed between 5 ounces and 15 ounces. Let x = salad plate filling weight, find the expected Value and the Variance of x. What is the probability hat a customer will take between 12 and 15 ounces of salad? 3. The average number of donuts a nine-year old child eats per month is uniformly distributed from 0.5 to 4 donuts, inclusive. Determine the probability that a randomly selected nine-year old child eats an average of; a) more than two donuts b) more than two donuts given that his or her amount is more than 1.5 donuts. 4. Starting at 5 pm every half hour there is a flight from Nairobi to Mombasa. Suppose that none of these plane tickets are completely sold out and they always have room for passagers. A person who wants to fly to Mombasa arrives at the airport at a random time between 8.45 AM and (.45 AM. Determine the probability that he waits for a) At most 10 minutes b) At least 15 minutes 2.2.2 Exponential Distribution The exponential distribution is often concerned with the amount of time until some specific event occurs. For example, the amount of time (beginning now) until an earthquake occurs has an exponential distribution. Other examples include the length, in minutes, of long distance business telephone calls, and the amount of time, in months, a car battery lasts. It can be shown, too, that the amount of change that you have in your pocket or purse follows an exponential distribution. Values for an exponential random variable occur in the following way. There are fewer large values and more small values. For example, the amount of money customers spend in one trip to the supermarket follows an exponential distribution. There are more people that spend less money and fewer people that spend large amounts of money. The exponential distribution is widely used in the field of reliability. Reliability deals with the amount of time a product lasts