Bellringer
Find the indicated term.
a.
0

4

4

C4 ( m ) (−4n ) = 256n

4

b.
4

5

1

C1 ( v ) (−u)

4

= −5v u

c.
4

6

C2 ( 2y ) ( x )

2

4

= 240y x

2

Homework Answers (8 – 6)
1. x3 + 3x2y + 3xy2 + y3
2. 16x4 + 32x3y + 24x2y2 + 8xy3 + y4
3. m3 + 9m2n + 27mn2 + 27n3
4. p5 + 5p4q + 10p3q2 + 10p2q3 + 5pq4 + q5
5. a. 0.015
b. 0.13`

6. a. 0.004
b. 0.33

7. 0.17

8. 0.65

8 – 7 Fitting to a Normal Distribution
A normal curve is used in a wide variety of situations to estimate probabilities. Before we examine exactly what a normal curve is, we will recap how it is related to what we’ve already learned.
Say you were rolling a die for a binomial experiment. There is a random variable associated with the outcomes of the experiment that we can calculate the probabilities for using the equations from the last section.
A probability distribution shows the probabilities that correspond to the possible values of a random variable.

Probability Distribution
In a binomial experiment, there are only a finite number of outcomes to the experiment. We can graph the probability of 0 successes,
1 success, 2 successes…etc to get a binomial distribution.
However, in continuous probability distribution, from more complex experimental data, would be a smooth curve where the outcome can be any number.

Normal curves
You may be familiar with the bell-shaped curve called the normal curve.
A normal distribution is a function of the mean and standard deviation of a data set that assigns probabilities to intervals of real numbers associated with continuous random variables.

How the Normal Curve Works
In a normal distribution, the probability of a value occurring is based its position in the curve relative to the mean. The curve is evenly distributed so that a certain amount of the data will lie under a particular portion of the graph.
68%-95%-99.7% Rule
• About 68% of the data will