Suppose that you are told that X is a normally distributed random variable with mean 1000. You are told that the 80% confidence interval around X is given by (975, 1025). What is standard deviation of X? (Provide your answer with two decimal places, rounding up, as in xx.xx) A random sample of 49 house prices is obtained in a small Midwestern city. A local real estate broker has claimed that the (population) mean house price is $80,000, with a variance of 100,000,000. If the real estate broker is correct, determine the probability that the sample mean is greater than $83,000. (Provide your answer with three decimal places, rounding up, as in x.xxx) The annual snowfall at a particular city is modeled as a normal random variable with a mean = 60 inches and a standard deviation = 20. What is the probability that this year's snowfall will be between 40 and 60 inches? (Provide your answer with four decimal places, rounding up, as in x.xxxx)