Question: The average yearly rainfall for Springfield follows a normal distribution with a mean of 55 inches and standard deviation 4.5 inches. (a) Find the probability

The average yearly rainfall for Springfield follows a normal distribution with a mean of 55 inches and standard deviation 4.5 inches. (a) Find the probability that Springfield has an average yearly rainfall between 49 and 61 inches. Include a sketch of the distribution with the mean and three standard deviations. Shade the region corresponding to the probability. (b) What percentage of years does Springfield have an average rainfall which is 50 inches or less? (c) Suppose that, in the year 2021, the average rainfall in Springfield was 42 inches. Compute the standard score (z-score) for this year and explain if this observation would be considered an outlier. (d) Consider the following statement: "10% of the time, the average rainfall in Springfield greater than or equal to X inches." Solve for X

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