Math

CalculusCalculus: An Applied Approach (MindTap Course List)Using the Exponential Density Function In Exercises 33-36, find the required probabilities using the exponential probability density function f ( t ) = 1 λ e − t / λ , [ 0 , ∞ ) Useful Life The time t (in years) until failure of a component in a machine is exponentially distributed with λ = 3.5 . Find the probability that the lifetime of a given component will be (a) less than 1 year, (b) more than 2 years but less than 4 years, and (c) at least 5 years.BuyFind*launch*

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9.2, Problem 36E

Textbook Problem

**Using the Exponential Density Function** In Exercises 33-36, find the required probabilities using the *exponential probability density function*

**Useful Life** The time *t* (in years) until failure of a component in a machine is exponentially distributed with

Calculus: An Applied Approach (MindTap Course List)

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...

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