5.1 - 5.2 Continuous Probability Distributions

Question 1

Normal Distribution

Answer 1

• A continuous probability distribution for a random variable, x.
• Graph is called the normal curve. (bell curve)

Question 2

Properties of a Normal Distribution

Answer 2

1. The mean, median, and mode are equal.
2. The normal curve is bell-shaped and is symmetric about the men.
3. The total area under the normal curve is equal to one.
4. The normal curve approaches, but never touches the x-axis as it extends farther and farther away from the mean.
5. Between μ - σ and μ + σ (in the center of the curve), the graph curves downward. The graph curves upward to the left of μ - σ and to the right of μ + σ. The points at which the curving downward are called the injection points.

Question 3

Means and Standard Deviations

Answer 3

• A normal distribution can have any mean and any positive standard deviation.
• The mean gives the location of the line of symmetry.
• The standard deviation describes the spread of the data.

Question 4

Empirical Rules - MEMORIZE

Answer 4

• About 68% lies between μ - σ and μ + σ
• About 95% lies between μ - 2σ and μ + 2σ
• About 99.7% lies between μ - 3σ and μ + 3σ

Question 5

Standard Normal Deviation

Answer 5

• A normal distribution with a mean of and a standard deviation of 1.
• Any x - value can be transformed into a z-score by using the formula.
  z = value - mean / standard deviation
  x - μ / σ

Question 6

The Standard Normal Distribution

Answer 6

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The total area under it’s normal curve is 1.

Question 7

Eliminating probability or finding area using a standard normal distribution

Answer 7

• Draw a bell curve; shade it; calculate area using table or graphing calculator.
• Cannot be a negative number.