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
