Question

1. Assume that X ∼ N(μ,σ). For each of the following, the generic number c is a number bigger than μ.

   1. (a) Write down the statement: “What is the probability that X is greater than c?” using P ( ) notation. Draw a picture of shaded curve.

   2. (b) Rewrite A) by standardizing X (turning it into Z). Hint: you will still have μ, σ, and c in the expression

   3. (c) Redo questions (a) and (b) for the statement: “What is the probability that X ̄ greater than c?” Draw a picture of the shaded curve (it should look different than A) ).

   4. (d) How do your z-scores compare in (b) versus (c)? What is the difference?

   5. (e) Draw the distribution of X and the distribution of X ̄ on the same plot together. What is the difference?

   6. (f) Are we more likely to observe an individual with a value far from the population mean or a sample mean with a value far from the population mean? Why?

Answer 1