http://www.ck12.org Chapter 5. Normal Distribution
With a probability of approximately 0.045, we could say it is rather unlikely (only about 5% of the time) that we
would find an iguana this small.
Lesson Summary
In order to find the percentage of data in between two values (or the probability of a randomly chosen value being
between those values) in a normal distribution, we can use thenormalcdfcommand on the TI-83/84 calculator.
When you know the percentage or probability, use theinvNormcommand to find az−score or value of the variable.
In order to use these tools in real situations, we need to know that the distribution of the variable in question
is approximately normal. When solving problems using normal probabilities, it helps to draw a sketch of the
distribution and shade the appropriate region.
Points to Consider
- How do the probabilities of a standard normal curve apply to making decisions about unknown parameters for
a population given a sample?
Review Questions
- Which of the following intervals contains the middle 95% of the data in a standard normal distribution?
a.z< 2
b.z≤ 1. 645
c.z≤ 1. 96
d.− 1. 645 ≤z≤ 1. 645
e.− 1. 96 ≤z≤ 1. 96 - For each of the following problems,xis a continuous random variable with a normal distribution and the
given mean and standard deviation.Pis the probability of a value of the distribution being less thanx. Find
the missing value and sketch and shade the distribution.
a.
mean Standard deviation x P
85 4. 5 0. 68
b.
mean Standard deviation x P
1 16 0. 05
c.
mean Standard deviation x P
73 85 0. 91
d.
mean Standard deviation x P
93 5 0. 90