Chapter 6: Normal Probability Distributions

Question 1

Properties of a Normal Distribution

Answer 1

1. A normal distribution is bell-shaped and symmetric about its mean.
2. A normal distribution is completely defined by its mean, μμ, and standard deviation, σσ.
3. The total area under a normal distribution curve equals 11.
4. The x-axis is a horizontal asymptote for a normal distribution curve.

Question 2

How do you determine if a distribution is normal?

Answer 2

• data must be continuous
• the distribution must be bell-shaped

Question 3

Properties of the Standard Normal Distribution

Answer 3

same as a normal distribution, except μ = 0 and σ = 1

Question 4

How do you standardize a normal distribution?

Answer 4

convert the random variable X to a z-score (round to two decimal places)

Question 5

finding the area under a curve

Answer 5

• value to the left of z or -z can be found on the table or via normalcdf (-1E99,z)
• value to the right of z = area to the left of -z, and vice versa