BuyFind*arrow_forward*

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 45RE

Textbook Problem

1 views

**Finding the Mean and Median** In Exercises 45–48, find the mean and median of the probability density function.

To determine

**To calculate:** The mean and median of probability density function

**Given Information:**

The probability density function is defined as

**Formula used:**

Mean:

If *f* is the probability density function *f* for a continuous random variable *x* for the interval *a* and *b* are real numbers, then the mean of *x* is defined by the formula,

Median:

If *f* is the probability density function *f* for a continuous random variable *x* for the interval *a* and *b* are real numbers, then the median of *x* is defined by the formula,

**Calculation:**

Consider the provided probability density function.

Use the formula

So,

Use the formula

Calculus: An Applied Approach (MindTap Course List)

Show all chapter solutions

Ch. 9.1 - Checkpoint 1 Worked-out solution available at...Ch. 9.1 - Two coins are tossed. A random variable assigns...Ch. 9.1 - Checkpoint 3 Worked-out solution available at...Ch. 9.1 - Checkpoint 4 Worked-out solution available at...Ch. 9.1 - Over a period of one year, a salesperson worked...Ch. 9.1 - Find the variance and standard deviation of the...Ch. 9.1 - In Exercises 1 and 2, solve for x. 19+23+29=xCh. 9.1 - In Exercises 1 and 2, solve for x....Ch. 9.1 - In Exercises 3-6, evaluate the expression....Ch. 9.1 - In Exercises 3-6, evaluate the expression....

Ch. 9.1 - In Exercises 3-6, evaluate the expression....Ch. 9.1 - In Exercises 3-6, evaluate the expression....Ch. 9.1 - In Exercises 7-10, write the fraction as a...Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Frequency and Probability Distributions In...Ch. 9.1 - Finding Frequency and Probability Distributions In...Ch. 9.1 - Random Selection In a class of 72 students, 44 are...Ch. 9.1 - Random Selection A card is chosen at random from a...Ch. 9.1 - Determining a Missing Probability In Exercises 9...Ch. 9.1 - Determining a Missing Probability In Exercises 9...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Using Probability Distributions In Exercises...Ch. 9.1 - Using Probability Distributions In Exercises 1518,...Ch. 9.1 - Using Probability Distributions In Exercises...Ch. 9.1 - Using Probability Distributions In Exercises...Ch. 9.1 - Health The table shows the probability...Ch. 9.1 - Children The table shows the probability...Ch. 9.1 - Biology Consider a couple who have four children....Ch. 9.1 - Die Roll Consider the experiment of rolling a...Ch. 9.1 - Finding Expected Value, Variance, and Standard...Ch. 9.1 - Finding Expected Value, Variance, and Standard...Ch. 9.1 - Finding Expected Value, Variance, and Standard...Ch. 9.1 - Finding Expected Value, Variance, and Standard...Ch. 9.1 - Finding Mean, Variance, and Standard Deviation In...Ch. 9.1 - Finding Mean, Variance, and Standard Deviation In...Ch. 9.1 - Revenue A publishing company introduces a new...Ch. 9.1 - Personal Income The probability distribution of...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - Baseball A baseball fan examined the record of a...Ch. 9.1 - Games of Chance If x is a players net gain in a...Ch. 9.1 - Games of Chance If x is a players net gain in a...Ch. 9.1 - Market Analysis A sporting goods company has...Ch. 9.1 - Market Analysis Repeat Exercise 37 for the case in...Ch. 9.2 - Show that f(x)=12x is a probability density...Ch. 9.2 - Show that f(x)=2e2x is a probability density...Ch. 9.2 - Find the probability that x lies in the interval...Ch. 9.2 - A probability density function is defined over the...Ch. 9.2 - For the function in Example 5. find the...Ch. 9.2 - In Exercises 1-4, determine whether the function...Ch. 9.2 - In Exercises 1-4, determine whether the function...Ch. 9.2 - In Exercises 1-4, determine whether the function...Ch. 9.2 - In Exercises 1-4, determine whether the function...Ch. 9.2 - In Exercises 5-7, evaluate the definite or...Ch. 9.2 - In Exercises 5-7, evaluate the definite or...Ch. 9.2 - In Exercises 5-7, evaluate the definite or...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Verifying a Probability Density Function In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Identifying Probability Density Functions In...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Finding a Probability A probability density...Ch. 9.2 - Finding a Probability A probability density...Ch. 9.2 - Waiting Time Buses arrive and depart from a...Ch. 9.2 - Demand The daily demand for gasoline x (in...Ch. 9.2 - Learning Theory The time t (in hours) required for...Ch. 9.2 - HOW DO YOU SEE IT? The graph shows two models for...Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Meteorology A meteorologist predicts that the...Ch. 9.2 - Demand The weekly demand x (in tons) for a certain...Ch. 9.2 - Demand Using the probability density function in...Ch. 9.3 - Find the expected value of the probability density...Ch. 9.3 - Find the variance and standard deviation of the...Ch. 9.3 - Use a symbolic integration utility to find the...Ch. 9.3 - Find the mean and median of the probability...Ch. 9.3 - Find the expected value and standard deviation of...Ch. 9.3 - Find the probability that a person selected at...Ch. 9.3 - Checkpoint 7 Worked-out solution available at...Ch. 9.3 - In Exercises 1 and 2, use integration by parts to...Ch. 9.3 - In Exercises 1 and 2, use integration by parts to...Ch. 9.3 - In Exercises 3 and 4, evaluate the definite...Ch. 9.3 - In Exercises 3 and 4, evaluate the definite...Ch. 9.3 - In Exercises 5 and 6, find each probability using...Ch. 9.3 - In Exercises 5 and 6, find each probability using...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Using two Methods In Exercises 1316, find the...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Using Technology In Exercises 17-22, use a...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Finding the Mean and Median In Exercises 23-28,...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Special Probability Density Functions In Exercises...Ch. 9.3 - Finding Probabilities In Exercises 35 and 36, let...Ch. 9.3 - Finding Probabilities In Exercises 35 and 36, let...Ch. 9.3 - Consumer Trends The number of coupons x used by a...Ch. 9.3 - Cost The daily cost x (in dollars) of electricity...Ch. 9.3 - Useful Life The useful lifetime of a product is...Ch. 9.3 - Useful Life The useful lifetime of a product is...Ch. 9.3 - Transportation The arrival time t (in minutes) of...Ch. 9.3 - Transportation Repeat Exercise 41 for a bus that...Ch. 9.3 - Useful Life The time t (in years) until failure of...Ch. 9.3 - Useful Life The time t (in years) until failure of...Ch. 9.3 - Waiting Time The waiting time t (in minutes) for...Ch. 9.3 - License Renewal The waiting time t (in minutes) at...Ch. 9.3 - Demand The daily demand x for a certain product...Ch. 9.3 - Demand Repeat Exercise 47 for the probability...Ch. 9.3 - Demand The daily demand x for water (in millions...Ch. 9.3 - HOW DO YOU SEE IT? In chemistry, the probability...Ch. 9.3 - Wages The employees of a large corporation are...Ch. 9.3 - Medical Science A medical research team has...Ch. 9.3 - Education For high school graduates from 2012...Ch. 9.3 - Fuel Mileage Assume the fuel mileages of all 2015...Ch. 9 - Finding Sample Spaces and Events In Exercises 14,...Ch. 9 - Finding Sample Spaces and Events In Exercises 14,...Ch. 9 - Finding Sample Spaces and Events In Exercises 14,...Ch. 9 - Finding Sample Spaces and Events In Exercises 14,...Ch. 9 - Frequency Distributions In Exercises 5 and 6,...Ch. 9 - Frequency Distributions In Exercises 5 and 6,...Ch. 9 - Bar Code Use the frequency distribution in...Ch. 9 - Kittens Use the frequency distribution in Exercise...Ch. 9 - Identifying Probability Distributions In Exercises...Ch. 9 - Identifying Probability Distributions In Exercises...Ch. 9 - Using Probability Distributions In Exercises 11...Ch. 9 - Using Probability Distributions In Exercises 11...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Revenue A publishing company introduces a new...Ch. 9 - Raffle A service organization is selling $5 raffle...Ch. 9 - Consumer Trends The probability distribution of...Ch. 9 - Vital Statistics The probability distribution of...Ch. 9 - Verifying a Probability Density Function In...Ch. 9 - Verifying a Probability Density Function In...Ch. 9 - Verifying a Probability Density Function In...Ch. 9 - Verifying a Probability Density Function In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Identifying Probability Density Functions In...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Finding a Probability In Exercises 31-36, sketch...Ch. 9 - Waiting Time The waiting time t (in minutes) for...Ch. 9 - Medicine The time t (in days) until recovery after...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding Expected Value, Variance, and Standard...Ch. 9 - Finding the Mean and Median In Exercises 4548,...Ch. 9 - Finding the Mean and Median In Exercises 4548,...Ch. 9 - Finding the Mean and Median In Exercises 4548,...Ch. 9 - Finding the Mean and Median In Exercises 4548,...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Special Probability Density Functions In Exercises...Ch. 9 - Transportation The arrival time t (in minutes) of...Ch. 9 - Transportation Repeat Exercise 55 for a train that...Ch. 9 - Waiting Time The waiting time t (in minutes) for...Ch. 9 - Useful Life The time t (in hours) until failure of...Ch. 9 - Demand The daily demand x for a certain product...Ch. 9 - Demand Repeat Exercise 59 for the probability...Ch. 9 - Education In 2013, the scores on the Medical...Ch. 9 - Botany In a botany experiment, plants are grown in...Ch. 9 - Four students answer a true-false question on an...Ch. 9 - A card is chosen at random from a standard 52-card...Ch. 9 - In Exercises 3 and 4, sketch a graph of the...Ch. 9 - In Exercises 3 and 4, sketch a graph of the...Ch. 9 - In Exercises 5 and 6, find the expected value,...Ch. 9 - In Exercises 5 and 6, find the expected value,...Ch. 9 - In Exercises 79, use a graphing utility to graph...Ch. 9 - In Exercises 79, use a graphing utility to graph...Ch. 9 - In Exercises 79, use a graphing utility to graph...Ch. 9 - In Exercises 1012, use the given probability...Ch. 9 - In Exercises 1012, use the given probability...Ch. 9 - In Exercises 1012, use the given probability...Ch. 9 - In Exercises 1315, use the given probability...Ch. 9 - In Exercises 1315, use the given probability...Ch. 9 - In Exercises 1315, use the given probability...Ch. 9 - An intelligence quotient or IQ is a number that is...

Find more solutions based on key concepts

Show solutions Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Applied Calculus

Factoring Common Factor Factor out the common factor. 63. 2x3 + x

Precalculus: Mathematics for Calculus (Standalone Book)

A tank full of water has the shape of a paraboloid of revolution as shown in the figure; that is, its shape is ...

Calculus: Early Transcendentals

Evaluate expressions in Exercises 3756, rounding your answer to four significant digits where necessary. 8643

Finite Mathematics and Applied Calculus (MindTap Course List)

Collinear Points In Exercises 65 and 66, determine whether the points are collinear. (Three points are collinea...

Calculus: Early Transcendental Functions

Use the guidelines of this section to sketch the curve. y = arctan(ex)

Single Variable Calculus: Early Transcendentals, Volume I

(a) Show that the parametric equations x =asinucosv,y=bsin u sinv, z = ccos u, 0 u , 0 v 2, represent an ell...

Multivariable Calculus

Find the median for the distribution of scores in the following frequency distribution table. X f 6 1 5 1 4 4 3...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

You have developed a series of questions to measure job satisfaction of bus drivers in New York City. A random ...

Essentials Of Statistics

In Exercises 73-80, find the indicated limits, if they exist. 77. limxx4+1x31

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Determine whether statement is true or false. If it is true, explain why. If it is false, explain why or given ...

Calculus (MindTap Course List)

Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?

Statistics for The Behavioral Sciences (MindTap Course List)

Critical Thinking Consider a data set with at least three data values. Suppose the highest value is increased b...

Understanding Basic Statistics

Prove the statement using the , definition of a limit. 29. limx2(x24x+5)=1

Single Variable Calculus

For problems 27-54, simplify each of the numerical expressions. Objective 2 and 3 2(3)22(2)36(1)5

Intermediate Algebra

Determine the nth-term formula for the number of square tiles in the nth figure.

Mathematical Excursions (MindTap Course List)

Rationalize each of the following denominators and simplify. (a) 5xy2x (b) yxxy23

Mathematical Applications for the Management, Life, and Social Sciences

The mode of a numerical data set is the value that occurs most frequently in the set. a. Determine the mode for...

Probability and Statistics for Engineering and the Sciences

Sketch the graphs of the equations in Exercises 512. 2y+x=1

Finite Mathematics

Find all points of intersection of the given curves. 38. r = 1 + cos , r = 1 sin

Single Variable Calculus: Early Transcendentals

Use the drawing provided to show that the area of the isosceles triangle is A=s2sincos

Elementary Geometry For College Students, 7e

For the following statements, underline the key words and translate into equations.
31. 4 more than 5 times a n...

Contemporary Mathematics for Business & Consumers

Simplify: (4y3+3y5)(2y34y22y+6)

Elementary Technical Mathematics

Consider the following polynomial over Z9, where a is written for [ a ] in Z9: f(x)=2x3+7x+4, g(x)=4x2+4x+6, h(...

Elements Of Modern Algebra

Identify the argument of each function. cot(2x+)

Trigonometry (MindTap Course List)

Using the Mean Value Theorem In Exercises 57-62, use a graphing utility to (a) graph the function f on the give...

Calculus: Early Transcendental Functions (MindTap Course List)

Finding Equations of Tangent Lines Graph the two parabolas y=x2andy=x2+2x5 in the same coordinate plane. Find e...

Calculus of a Single Variable

In Exercises 118, determine whether each system of linear equations has a one and only one solution, b infinite...

Finite Mathematics for the Managerial, Life, and Social Sciences

Classify as true or false: a If the vertex angles of two isosceles triangles are congruent, the triangles are s...

Elementary Geometry for College Students

Using Stokes Theorem In Exercises 7-16, use Stokes Theorem to evaluate cFdr. In each case, C is oriented counte...

Multivariable Calculus

0
1
does not exist

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

By the method of undetermined coefficients, a particular solution to y″ − 5y′ + 6y = e4x will have the form:
yp...

Study Guide for Stewart's Multivariable Calculus, 8th

Finding a Derivative In Exercises 9-34, find the derivative of the function. y=(2x7)3

Calculus (MindTap Course List)

Consider the following hypothesis test. H0:d0Ha:d0 The following data are from matched samples taken from two p...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In exercise 4, the following estimated regression equation relating sales to inventory investment and advertisi...

Statistics for Business & Economics, Revised (MindTap Course List)

Applications Population of a city The population Pt, of a small city can be approximated by the exponential fun...

College Algebra (MindTap Course List)

Express these ratios in lowest fractional form. 1. 15:32

Mathematics For Machine Technology

It has been demonstrated that students with high self-esteem tend to have higher grades than students with low ...

Research Methods for the Behavioral Sciences (MindTap Course List)

In Exercises4346, use the following information: A super market polled 1000 customers regarding the size of the...

Mathematics: A Practical Odyssey

In a study of a proposed treatment for diabetes prevention, 339 people under the age of 20 who were thought to ...

Introduction To Statistics And Data Analysis

In addition to the key words, you should be able to define each of the following terms: literature search title...

Research Methods for the Behavioral Sciences (MindTap Course List)