1. Suppose that the scores obtained in a college entrance exam are normally distributed with a mean of 450 and a standard deviation of 100. a. What percentage of test takers will score between 400 and 500? b. If the score a student gets is 630. What percent of the students taking the test will have a higher score? c. What percentage will score less than or equal to 630? 2. The U.S. Bureau of Labor Statistics reports that the average annual food and beverage expenditure for a household is $5,700. Assume that annual food and beverage expenditures are normally distributed and that the standard deviation is $1,500. a. What percentage of families spend more than $7,000 annually on food and beverages? b. What percentage of households spend $4,200 or less annually on food and beverages? 3. The inter-arrival times of patients in an emergency room follow an exponential probability distribution, whose mean is 30 minutes. a. What is the probability that the inter-patient arrival times are 30 minutes or less? b. What is the probability that inter-patient arrival times are 20 minutes or less? c. What is the probability that more than one hour elapses between arrival times? 4. The lifetime (in hours) of an electronic device is a random variable that has an exponential probability density function. The mean lifetime of this device is 50 hours. a. What is the probability that the device will have a failure in the first 25 hours of operation (25 hours or less)? b. What is the probability that the device will operate more than 100 hours without failure