   Chapter 7.3, Problem 25E

Chapter
Section
Textbook Problem

Refer to the probability distribution given in the previous exercise. Put the following probabilities in order, from smallest to largest:P(2 < x < 3), P(2 ≤ x ≤ 3), P(x ＜ 2), P(x > 7)Explain your reasoning.7.24 A particular professor never dismisses class early. Let x denote the amount of time past the class end time (in minutes) that passes before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 minutes. The density curve is shown in the following figure: a. What is the probability that at most 5 minutes pass before dismissal? (Hint: See Example 7.8.) b. What is the probability that between 3 and 5 minutes pass before dismissal?

To determine

Arrange the probabilities from smallest to largest.

Explanation

Calculation:

It is given that a professor does not dismisses the class early. Define the random variable x as the amount of time past the class end time (in minutes) that passes before the professor dismisses the class. The random variable x follows uniform distribution on the interval 0 to 10 minutes. Also, the density curve is provided.

The area under the density curve represents a rectangle. The probability can be obtained by using the area of the rectangle. That is, Area=(Base)(Height).

Here, the curve has a positive height of 110 between 0 and 10.

The probability is obtained by finding the area between x=2 and x=3.

P(2<x<3)=(Base)(Height)=(32)(110)=110=0.1

The random variable x represents a continuous random variable. Thus, for a continuous random variable, P(a<x<b)=P(axb).

P(2x3)=P(2<x<3)=0

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 9 and 10, find the limit. limx3(2x23x+4)

Calculus: An Applied Approach (MindTap Course List)

limx6(x210x)=. a) 24 b) 6 c) 26 d) does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Convert the expressions in Exercises 6584 to power form. 35x2

Finite Mathematics and Applied Calculus (MindTap Course List)

Given: ABC with BDCE m3=m4=30m1=m2=70 Find: mB

Elementary Geometry for College Students

Rewritten in reverse order,

Study Guide for Stewart's Multivariable Calculus, 8th 