Problem-1 A random variable is normally distributed with a mean of p = 50 and a standard deviation of o = 5. a) Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. b) What is the probability the random variable will assume a value between 45 and 55? c) What is the probability the random variable will assume a value between 40 and 60? Problem-2 Given a standard normal random variable (2 values) or probabilities, compute the following probabilities or 2 values, as applicable. a) P (0 s z s 0.83) b) P (1.57 s z 0.44) d) The area to the left of z is 0.975 e) The area between 0 and z is 0.45