Chapter 7.3, Problem 25E

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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,

Here, the curve has a positive height of

The probability is obtained by finding the area between

The random variable *x* represents a continuous random variable. Thus, for a continuous random variable,

Sect-7.1 P-1ESect-7.1 P-2ESect-7.1 P-3ESect-7.1 P-4ESect-7.1 P-5ESect-7.1 P-6ESect-7.1 P-7ESect-7.2 P-8ESect-7.2 P-9ESect-7.2 P-10E

Sect-7.2 P-11ESect-7.2 P-12ESect-7.2 P-13ESect-7.2 P-14ESect-7.2 P-15ESect-7.2 P-16ESect-7.2 P-17ESect-7.2 P-18ESect-7.2 P-19ESect-7.2 P-20ESect-7.2 P-21ESect-7.3 P-22ESect-7.3 P-23ESect-7.3 P-24ESect-7.3 P-25ESect-7.3 P-26ESect-7.3 P-27ESect-7.3 P-28ESect-7.3 P-29ESect-7.3 P-30ESect-7.3 P-31ESect-7.3 P-32ESect-7.4 P-33ESect-7.4 P-34ESect-7.4 P-35ESect-7.4 P-36ESect-7.4 P-37ESect-7.4 P-38ESect-7.4 P-39ESect-7.4 P-40ESect-7.4 P-41ESect-7.4 P-42ESect-7.4 P-43ESect-7.4 P-44ESect-7.4 P-45ESect-7.4 P-46ESect-7.4 P-47ESect-7.4 P-48ESect-7.4 P-49ESect-7.4 P-50ESect-7.5 P-51ESect-7.5 P-53ESect-7.5 P-54ESect-7.5 P-55ESect-7.5 P-56ESect-7.5 P-57ESect-7.5 P-58ESect-7.5 P-59ESect-7.5 P-60ESect-7.5 P-61ESect-7.5 P-62ESect-7.5 P-63ESect-7.5 P-64ESect-7.5 P-65ESect-7.5 P-66ESect-7.5 P-67ESect-7.5 P-68ESect-7.5 P-69ESect-7.6 P-70ESect-7.6 P-71ESect-7.6 P-72ESect-7.6 P-73ESect-7.6 P-74ESect-7.6 P-75ESect-7.6 P-76ESect-7.6 P-77ESect-7.6 P-78ESect-7.6 P-79ESect-7.6 P-80ESect-7.6 P-81ESect-7.6 P-82ESect-7.6 P-83ESect-7.6 P-84ESect-7.6 P-85ESect-7.6 P-86ESect-7.6 P-87ESect-7.6 P-88ESect-7.6 P-89ESect-7.6 P-90ESect-7.6 P-91ESect-7.6 P-92ESect-7.6 P-93ESect-7.6 P-94ESect-7.6 P-95ESect-7.6 P-96ESect-7.7 P-97ESect-7.7 P-98ESect-7.7 P-99ESect-7.7 P-100ESect-7.7 P-101ESect-7.7 P-102ESect-7.7 P-103ESect-7.7 P-104ESect-7.7 P-105ESect-7.7 P-106ESect-7.7 P-107ESect-7.7 P-108ESect-7.8 P-109ESect-7.8 P-110ESect-7.8 P-111ESect-7.8 P-112ESect-7.8 P-113ESect-7.8 P-114ESect-7.8 P-115ESect-7.8 P-116ESect-7.8 P-117ESect-7.8 P-118ESect-7.8 P-119ESect-7.8 P-120ECh-7 P-121CRCh-7 P-122CRCh-7 P-123CRCh-7 P-124CRCh-7 P-125CRCh-7 P-126CRCh-7 P-127CRCh-7 P-128CRCh-7 P-129CRCh-7 P-130CRCh-7 P-131CRCh-7 P-132CRCh-7 P-133CRCh-7 P-134CRCh-7 P-135CRCh-7 P-136CRCh-7 P-137CRCh-7 P-138CRCh-7 P-139CRCh-7 P-140CRCh-7 P-141CRCh-7 P-2CRECh-7 P-3CRECh-7 P-5CRECh-7 P-6CRECh-7 P-7CRECh-7 P-8CRECh-7 P-9CRECh-7 P-10CRECh-7 P-11CRECh-7 P-12CRECh-7 P-13CRECh-7 P-14CRECh-7 P-15CRECh-7 P-16CRECh-7 P-17CRECh-7 P-18CRECh-7 P-19CRECh-7 P-20CRECh-7 P-21CRE

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