Question

We will use shorthand notation and probability notation for random variables when working with normally distributed random variables. 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).

Use this distribution of vitamin C content to answer the following questions:

1) What is the probability that a randomly selected orange will have less than 660 IU? Using X as the random variable, state your answer as a probability statement using the probability notation developed in the learning module.

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

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

4) 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 developed in the learning module.

5) Suppose Y~N( 280 mg, 20 mg). Find Y₁such that P( Y > Y₁) = 0.0250. State your answer in the form of a complete sentence without using any probability notation.

Answer 1