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Introduction To Statistics And Dat...

6th Edition
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ISBN: 9781337793612

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Chapter
Section
BuyFindarrow_forward

Introduction To Statistics And Dat...

6th Edition
PECK + 1 other
ISBN: 9781337793612
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:

images

  1. a. What is the probability that at most 5 minutes pass before dismissal? (Hint: See Example 7.8.)
  2. 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

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