Standard Normal Curve

Question 1

According to the National Center for Health Statistics, the mean height of an American male is 69.3 inches and the mean height of an American female is 63.8 inches. The standard deviation for both genders is 2.7 inches.

• According to Chebyshev’s Theorem 75% of the data for your gender lies between what two heights?
• If height is assumed to be normal, what percentage of the data lies between those same two heights?

NOTE: The normal distribution is really simple. Look at the standard normal curve and just add the values within 2 standard deviations from the mean.

Question 2

• What are the major categories of Federal government spending and revenue and of state/local government spending and revenue?
• What is the relationship between total utility, marginal utility, and the law of diminishing marginal utility?

Question 3

Imagine you are writing exam questions for an algebra course. You want to write questions that include finding the zeros of polynomials. To balance the difficulty level of the test’s questions, you decide to include two different types of questions, as described here:

• Question #1: A polynomial of degree at least 3 where all the zeros are positive whole numbers
• Question #2: A polynomial of degree at least 3 where one or more of the roots are fractions

Find two polynomials for the two described questions. Explain how you know each question satisfies the requirements stated. What approach did you use to find these polynomials?