Chapter 5: Continuous Random Variables
5.4 Using Technology for the Uniform Distribution
Learning Objectives
By the end of this section, the student should be able to:
- use technology to solve problems involving the Uniform Distribution
This is another section to show technology tools that can be used to help with the statistics concepts taught in this chapter. This section will cover tools to help solve problems involving the Uniform Distribution.
Graphing Calculator
Currently, the TI-83+ and TI-84 do not have built-in uniform probability distribution functions. We will have to rely on the additional technology tools to assist as with these problems.
Additional Technology Tools
In addition to the graphing calculator, there are some additional technology tools that can be used for the concepts covered on this page. Below are links to helpful videos for those tools:
- Desmos: (Desmos Graphing Calculator Link)
- Mean and Standard Deviation of a Uniform Distribution Using Desmos
- Uniform Distribution Notation and Probabilities: By Hand / Desmos
- Determine Uniform Random Variable Probabilities P(c<X<d) : By Hand/TI84/Desmos
- Determine Uniform Random Variable Probabilities P(X<c): By Hand/TI84/Desmos
- Determine Uniform Random Variable Probabilities P(X>c): By Hand/TI84/Desmos
- Uniform Distribution Probabilities Using Desmos
- Uniform Distribution Percentiles Using Desmos
- Microsoft Excel-Continuous Distributions
- Microsoft Excel-Uniform Distributions
Section Practice
A random number generator picks a number from one to nine in a uniform manner. You may find it helpful to sketch the graph and shade the area of interest.
- [latex]X \sim \underline{\hspace{2cm}}[/latex]
- Graph the probability distribution.
- [latex]f(x) = \underline{\hspace{2cm}}[/latex]
- [latex]\mu = \underline{\hspace{2cm}}[/latex]
- [latex]\sigma = \underline{\hspace{2cm}}[/latex]
- [latex]P(3.5 \lt x \lt 7.25)= \underline{\hspace{2cm}}[/latex]
- [latex]P(x > 5.67)= \underline{\hspace{2cm}}[/latex]
- [latex]P(x >5 | x > 3) = \underline{\hspace{2cm}}[/latex]
- Find the 90th percentile.
Solution
- [latex]X \sim U(1,9)[/latex]
- Check student’s solution.
- [latex]f\left(x\right)=\frac{1}{8}[/latex] where [latex]1\le x\le 9[/latex]
- five
- 2.3
- [latex]\frac{15}{32}[/latex]
- [latex]\frac{333}{800}[/latex]
- [latex]\frac{2}{3}[/latex]
- 8.2
According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. Let’s suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month. You may find it helpful to sketch the graph and shade the area of interest.
- Define the random variable. [latex]X = \underline{\hspace{2cm}}[/latex]
- [latex]X \sim \underline{\hspace{2cm}}[/latex]
- Graph the probability distribution.
- [latex]f(x) = \underline{\hspace{2cm}}[/latex]
- [latex]\mu = \underline{\hspace{2cm}}[/latex]
- [latex]\sigma = \underline{\hspace{2cm}}[/latex]
- Find the probability that the individual lost more than ten pounds in a month.
- Suppose it is known that the individual lost more than ten pounds in a month. Find the probability that he lost less than 12 pounds in the month.
- [latex]P(7 \lt x \lt 13 | x > 9) = \underline{\hspace{2cm}}[/latex]. State this in a probability question, similarly to parts 7 and 8, draw the picture, and find the probability.
The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. We randomly select one first grader from the class. You may find it helpful to sketch the graph and shade the area of interest.
- Define the random variable. [latex]X = \underline{\hspace{2cm}}[/latex]
- [latex]X \sim \underline{\hspace{2cm}}[/latex]
- Graph the probability distribution.
- [latex]f(x) = \underline{\hspace{2cm}}[/latex]
- [latex]\mu = \underline{\hspace{2cm}}[/latex]
- [latex]\sigma = \underline{\hspace{2cm}}[/latex]
- Find the probability that she is over 6.5 years old.
- Find the probability that she is between four and six years old.
- Find the 70th percentile for the age of first graders on September 1 at Garden Elementary School.
