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Sec. 5.1 β Introduction to the Normal Distribution In chapter four you studied _________ probability distributions. Chapter five covers the ___________ distribution, which is the most important ___________ probability distribution. A ___________ _____________ is a continuous probability distribution for a random variable π₯. The graph of a normal distribution is called the __________ _________. A normal distribution has the following properties. 1. The mean, median, and mode are equal. 2. The normal curve is bell-shaped and is symmetric about the mean. 3. The total area under the normal curve is one. 4. The normal curve approaches, but never touches, the x-axis as it extends farther and farther away from the mean. 5. The graph has inflection points at π β π and π + π. The ____________ _____________ ______________ is when the mean is 0 and standard deviation is 1. All normal distributions can be βconvertedβ into the standard normal distribution using z-scores. Remember: π§= Note: Page 245 has excellent guidelines for finding areas under the normal curve. Find the area under the standard normal curve to the left of π§ = β0.99. Find the area under the standard normal curve to the right of π§ = 1.06. Find the area under the standard normal curve between π§ = β1.5 and π§ = 1.25. Find the area under the standard normal curve to the left of π§ = β1.3 and to the right of π§ = 1.92.