Download Graphs of Normal Probability Distributions

Graphs of Normal Probability Distributions:
Normal Distribution – one of the most important examples of a continuous probability
distribution, studied by Abraham de Moivre (1667 – 1754) and Carl Friedrich Gauss
(1777 – 1855). (Sometimes called the Gaussian distribution.)
We could look at a very complicated formula which speaks of the normal distribution,
however, we will just look at the graph of a normal distribution to get a better idea of
what we are discussing.
Normal Curve – graph of a normal distribution.
- bell-shaped curve.
*** View Figure 6 – 1 (text p. 327).
Parameters which control the shape of the normal curve:
1) Mean (μ) – balance point.
2) Standard Deviation (σ) – measures the extent of the spread.
Important Properties of a Normal Curve:
1) The curve is “bell-shaped” with the highest point over the mean (μ).
2) It is symmetrical about a vertical line through μ.
3) The curve approaches the horizontal axis but never touches or crosses it.
4) The transition points between cupping upward and downward occur at (μ - σ)
and (μ – σ).
*** View Guided Exercise #1 (text p. 328).
*** View Guided Exercise #2 (text p. 328).
Figure 6-4 on text p. 329 gives examples of when normal curves have same μ’s but
different σ’s. It also gives examples of same σ’s, different μ’s.
*** View Guided Exercise #3 (text p. 329 – 330).
*** View Guided Exercise #4 (text p. 330).
Some Facts to Realize About Normal Curves:
1) The mean and standard deviation have no influence on each other. So, a curve
with a large mean need not have a large standard deviation.
2) If a curve is very spread out, it then has a large standard deviation, and vice
versa.
***Complete examples on text p. 342 – 343, #’s 1 – 4.
Examples:
Sketch the following curves given the information below. Label everything, including
transition points.:
a) Mean of 24 and Standard Deviation of 11.
b) Mean of 19 and Standard Deviation of 6.
c) Mean of 111 and Standard Deviation of 10.
d) Mean of 107.5 and Standard Deviation of 9.
e) Mean of 20 and Standard Deviation of 6.2.
f) Mean of 16 and Standard Deviation of 1.4.
g) Mean of 4 and Standard Deviation of 7.
h) Mean of -18 and Standard Deviation of 8.
i) Mean of 32 and Standard Deviation of 2.
j) Mean of 16.5 and Standard Deviation of 15.