An electrical resistor is a component in a circuit that slows down an electrical current. A particular resistor has a 56Ω (ohm) rating. The actual resistance value, X, varies according to a normal distribution with mean 56 and standard deviation 0.43. a) What is the probability that the actual resistance is between 56.5Ω and 57.3Ω ? [6pts] b) What is the value separating the lowest 15% of actual resistance values from the remaining values? [6pts] c) Suppose a random sample of 10 of these resistors are observed and the actual resistance values are recorded. Find the probability that the sample mean exceeds 55.75Ω. [6pt:] d) Suppose a random sample of 500 of these resistors are observed and the number, Y, with actual resistance values less than 56.5Ω is recorded. What is the (approximate) probability that at least 450 of these resistors have an actual resistance value less than 56.5Ω2 ? [6pts]