Question: 3. (a) Define standard normal variate. Write down the density function of standard normal distribution. What are the important properties of normal distribution? Write down

3. (a) Define standard normal variate. Write down the density function of standard normal distribution. What are the important properties of normal distribution? Write down the uses of normal distribution. (b) Suppose that the weight of navel oranges is normally distributed with mean u = 10 ounces, and standard deviation o = 2 ounces. We can write X ~ N(10, 2). Now find the following questions: a) What proportion of oranges weigh more than 1 1.0 ounces? b) What proportion of oranges weigh less than 8.5 ounces? C) What proportion of oranges weigh less than 5 ounces? d) What proportion of oranges weigh more than 5.5 ounces? e) What proportion of oranges weigh between 8.5 and 11.5 ounces

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