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 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.

(Attached is a screenshot of the exact question for more clarification) I hope this all makes sense and thank you for your help!

FORUM DESCRlPTION We made the shift from working with discrete random variables back in Unit 2 to now working with continuous random variables. Highly important for the rest of the course is our ability to use the Normal Distribution, in which we either find a probability from a range of values of the normally distributed variable X or we find a range of values from a given probability. We will use shorthand notation (review LM 09 for how to use this notation) and probability notation for random variables (review LM 09 and LM 07 as needed) 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: am 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. 3pt 2) What is the 80th percentile of the of the distribution of vitamin C content of the oranges? 1pt 3) What proportion of oranges exceed the vitamin C content you found in part (2) above? 3pt 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. Extra Credit: 3pt EC Suppose Y~N( 280 mg, 20 mg). Find Y1 such that P( Y > Y1) = 0.0250. State your answer in the form of a complete sentence without using any probability notation