2. Please illustrate your answers with a sketch of the relevant normal distribution. Please explain how you obtained the relevant probabilities (including whether you used a statistical table, R, Excel, a particular website, etc.) (3) Suppose that the temperature in Massachusetts in October is normally distributed with a mean of 65 and a standard deviation of 3. i. What is the probability that the temperature is less than 66? ii. What is the probability that the temperature is more than 60? iii. What is the probability that the temperature is between 64 and 70? (b) Suppose that height of 3 year olds in the United States is normally distributed with a mean of 38 inches and a variance of 16 inches squared. i. What fraction of 3 year olds are between 34 and 42 inches tall? ii. What fraction of 3 year olds are between 30 and 46 inches tall? iii. What fraction of 3 year olds are between 26 and 50 inches tall? iv. Discuss your answers in the context of the Empirical Rule. (c) Suppose that the distribution of starting salaries for Brandeis graduates is normally distributed with a mean of $50,000 and a standard deviation of $10,000. i. What salary corresponds to the 2.5th percentile of the salary distribution? ii. What salary corresponds to the 5th percentile of the salary distribution? iii. What salary corresponds to the 25th percentile of the salary distribution? iv. What salary corresponds to the 75th percentile of the salary distribution? v. What salary corresponds to the 95th percentile of the salary distribution? vi. What salary corresponds to the 97.5th percentile of the salary distribution? ((1) Suppose that the time students spend studying for economics classes is normally distributed with a mean of 9 hours per week. If 40% of students spend between 8 and 10 hours per week studying, what is the probability that a student spends more than 11 hours per week studying