1. Timber beams are widely used in home construction. When the load (measured in pounds) per unit length has a constant value over part of a beam, the load is said to be uniformly distributed over that part of the beam. Uniformly distributed beam loads were used to derive the stiffness distribution of the beam. Consider the cantilever beam with a uniformly distributed load between 100 and 115 pounds per linear foot. a. Draw the uniform distribution that describes this situation. b. What is the formula for the area of a rectangle? C. What is the probability that a beam load exceeds 110 pounds per linear foot? d. What is the probability that a beam load is less than 102 pounds per linear foot? e. Find a value L such that the probability that the beam load exceeds L is only .1. 2. Find each of the following probabilities for a standard normal variable z: a. P(z = 1) b. P(z1) c. P(z < 1) d. P(z > 1) e. P(-1z1) f. P(-2 3. Suppose x is a normally distributed random variable with = 11 and = 2. Find each of the following: a. P(10x12) b. P(6x10) c. P(x 13.24) d. P(x < 7.62) 4. Suppose x is a normally distributed random variable with = 30 and = 8. Find a value xo of the random variable x such that a. P(xx) = .5 b. P(x < x) = .025 c. P(x > x) = .1 d. P(x > xo) = .95 5. Miraculin - a protein naturally produced in a rare tropical fruit - can convert a sour taste into a sweet taste; thus, it has the potential to be an alternative low-calorie sweetener. A group of Japanese environmental scientists investigated the ability of a hybrid tomato plant to produce miraculin. For a particular generation of the tomato plant, the amount x of miraculin produced (measured in micrograms per gram of fresh weight) had a mean of 105.3 and a standard deviation of 8.0. Assume that x is normally distributed. a. Find P(x >120) b. Find P(100 < x < 110) C. Find a value of a for which P(x < a) = .25 6. Ambulance response time is measured as the time (in minutes) between the initial call to emergency medical services (EMS) and when the patient is reached by ambulance. An investigation was conducted on the characteristics of ambulance response time for EMS calls in Edmonton, Alberta. For a particular EMS station (Station A), ambulance response times were = 7.5 minutes and = 2.5 minutes. a. Regulations require that 90% of all emergency calls should be reached in 9 minutes or less. Are the regulations met at EMS Station A? Explain. b. A randomly selected EMS call in Edmonton has an ambulance response time of 2 minutes. Is it likely that this call was serviced by Station A? Explain.