Solution Found!
Uniform Distribution The random-number generator on
Chapter 7, Problem 17E(choose chapter or problem)
The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution.
(a) Draw the graph of the uniform density function.
(b) What is the probability of generating a number between 0 and 0.2?
(c) What is the probability of generating a number between 0.25 and 0.6?
(d) What is the probability of generating a number greater than 0.95?
(e) Use your calculator or statistical software to randomly generate 200 numbers between 0 and 1. What proportion of the numbers are between 0 and 0.2? Compare the result with part (b).
Questions & Answers
QUESTION:
The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution.
(a) Draw the graph of the uniform density function.
(b) What is the probability of generating a number between 0 and 0.2?
(c) What is the probability of generating a number between 0.25 and 0.6?
(d) What is the probability of generating a number greater than 0.95?
(e) Use your calculator or statistical software to randomly generate 200 numbers between 0 and 1. What proportion of the numbers are between 0 and 0.2? Compare the result with part (b).
ANSWER:Step 1 of 4
The random variable X follows the uniform distribution.
We have to find the following.
(a) The graph of the uniform distribution.
(b) The probability of generating a number between 0 and 0.2.
(c) The probability of generating a number between 0.25 and 0.6.
(d) The probability of generating a number greater than 0.95.
(e) The proportion of numbers between 0 and 0.2, after generating 200 numbers between 0 and 1.