W06 - Examples

Normal distribution

Basic generalized normal calculation

Suppose . Find .

Solution First write as a linear transformation of : Then:

Look in a table to find that and therefore:

Gaussian: interval of

Find the number such that .

Solution First convert the question: Solve for so that this value is :

Use a table to conclude .

Heights of American males

Suppose that the height of an American male in inches follows the normal distribution .

• (a) What percent of American males are over 6 feet, 2 inches tall?
• (b) What percent of those over 6 feet tall are also over 6 feet, 5 inches tall?

Solution (a) Let be a random variable measuring the height of American males in inches, so . Thus , and:

(b) We seek as the answer. Compute as follows:

Variance of normal from CDF table

Suppose , and suppose you know .

Find the approximate value of using a table.

Solution implies .

So and thus . Then: so .

Looking in the chart of for the nearest inverse of 0.8, we obtain , hence .