Download Sec. 5.1 – Introduction to the Normal Distribution

Sec. 5.1 – 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 𝑥. 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 𝜇 − 𝜎 and 𝜇 + 𝜎.
The ____________ _____________ ______________ is when the mean is 0 and
standard deviation is 1.
All normal distributions can be “converted” into the standard normal distribution
using z-scores. Remember:
𝑧=
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 𝑧 = −0.99.
Find the area under the standard normal curve to the right of 𝑧 = 1.06.
Find the area under the standard normal curve between 𝑧 = −1.5 and 𝑧 = 1.25.
Find the area under the standard normal curve to the left of 𝑧 = −1.3 and to the
right of 𝑧 = 1.92.