Answer Happy

A random variable is normally distributed with a mean of u = 90 and a standard deviation of c = 5. (a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 75 and 105). Areas under the Curve for any Normal Distribution 99,75 95.4% 65.3% 3 les + lo 1 . - 2 + 10 + 20 Sketch a normal curve for the probability density function. Label the horizontal axis with values of 75, 80, 85, 90, 95, 100, and 105. A 105 100 95 90 85 80 75 75 BO 85 90 95 100 195 80 90 100 105 95 85 75 75 85 95 105 100 90 50 © (b) What is the probability the random variable will assume a value between 0 and 100? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 75 and 105? (Round your answer to three decimal places.)