To represent normal variable (distribution) with mean ( µ) and standard deviation (σ) we use shorthand notation X ~ N (µ, σ). For example, suppose the vitamin C content of a particular variety of orange is distributed normally with mean 720 IU and standard deviation 46 IU. If we designate X = the vitamin C content of a randomly selected orange, then our shorthand notation is X~N(720 IU, 46 IU).
To represent probability between two values a and b we use notation P (a< X < b), to represent probability greater than a we use notation P(a>X), and to represent probability less than a, we use notation P(XUse the example and notation to answer the following questions:

2pt 1) What is the probability that a randomly selected orange will have less than 660 IU?

2 pt 2) Using X as the random variable, what probability notation would you use to represent the probability in part 1?

2pt 3) What is the 80th percentile of the distribution of vitamin C content of the oranges?

1pt 4) What proportion of oranges exceed the vitamin C content you found in part (2) above?

3pt 5) What range of vitamin C content values represent the middle 80% of the distribution? State your answer as a probability statement using the probability notation.