Explanation Given Information: The probability density function f ( x ) = 1 32 x over the interval [ 0 , 8 ] . Graph: Consider the provided probability density function. f ( x ) = 1 32 x Use the ti-83 graphing calculator to construct the graph of the function. Step 1: Open the ti-83 graphing calculator. Step 2: Press [Y=] and enter the function Y 1 = 1 32 x . Step 3: Press the [WINDOW] key and adjust the scale. X min = 0 X max = 10 X s c l = 1 And Y min = 0 Y max = 2 32 Y s c l = 0.01 Step 4: Press the [GRAPH] key. The graph of the function f ( x ) = 1 32 x is obtained as, Now, calculate the probabilities. Consider the provided probability density function f ( x ) = 1 32 x . Use the formula P ( c ≤ x ≤ d ) = ∫ c d f ( x ) d x to calculate the required probabilities. So, P ( c < x < d ) = ∫ c d 1 32 x d x Use the formula ∫ x n d x = x n + 1 n + 1 and integrate. ∫ c d 1 32 x d x = 1 32 ( x 2 2 ) c d = 1 64 ( x 2 ) c d (a) To calculate P ( 0 < x < 3 ) , use the Fundamental theorem ∫ a b f ( x ) d x = F ( b ) − F ( a ) and apply the limits on 1 64 ( x 2 ) c d . 1 64 ( x 2 ) 0 3 = 1 64 ( 3 2 − 0 ) = 9 64 Thus, the probability of P ( 0 < x < 3 ) is 9 64

WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term

10th Edition

ISBN: 9781337652308

Author: Ron Larson

Publisher: Brooks Cole

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Chapter 9, Problem 32RE

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To graph: The probability density function f(x)=132x over the interval [0,8] and calculate the probabilities (a) P(0<x<3) (b) P(x=7) (c) P(4<x<6) (d) P(x≥6).

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Chapter 9, Problem 31RE

Chapter 9, Problem 33RE

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Chapter 9 Solutions

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Ch. 9.1 - Checkpoint 1 Worked-out solution available at...Ch. 9.1 - Prob. 2CP Ch. 9.1 - Prob. 3CP Ch. 9.1 - Prob. 4CP Ch. 9.1 - Prob. 5CP Ch. 9.1 - Prob. 6CP Ch. 9.1 - Prob. 1SWU Ch. 9.1 - Prob. 2SWU Ch. 9.1 - Prob. 3SWU Ch. 9.1 - Prob. 4SWU

Ch. 9.1 - Prob. 5SWU Ch. 9.1 - Prob. 6SWU Ch. 9.1 - Prob. 7SWU Ch. 9.1 - Prob. 8SWU Ch. 9.1 - Prob. 9SWU Ch. 9.1 - Prob. 10SWU Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Random Selection A card is chosen at random from a...Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Using Probability Distributions In Exercises 1518,...Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Children The table shows the probability...Ch. 9.1 - Prob. 21E Ch. 9.1 - Die Roll Consider the experiment of rolling a...Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E 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 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.2 - Prob. 1CP Ch. 9.2 - Prob. 2CP Ch. 9.2 - Prob. 3CP Ch. 9.2 - Prob. 4CP Ch. 9.2 - Prob. 5CP Ch. 9.2 - Prob. 1SWU Ch. 9.2 - Prob. 2SWU Ch. 9.2 - Prob. 3SWU Ch. 9.2 - Prob. 4SWU Ch. 9.2 - Prob. 5SWU Ch. 9.2 - Prob. 6SWU Ch. 9.2 - Prob. 7SWU Ch. 9.2 - Prob. 1E Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - Prob. 11E Ch. 9.2 - Prob. 12E Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Prob. 15E Ch. 9.2 - Making a Probability Density Function In Exercises...Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Demand The daily demand for gasoline x (in...Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Prob. 34E Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Demand The weekly demand x (in tons) for a certain...Ch. 9.2 - Prob. 39E Ch. 9.3 - Prob. 1CP 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 - Prob. 4CP Ch. 9.3 - Prob. 5CP Ch. 9.3 - Prob. 6CP Ch. 9.3 - Prob. 7CP Ch. 9.3 - Prob. 1SWU Ch. 9.3 - Prob. 2SWU Ch. 9.3 - Prob. 3SWU Ch. 9.3 - Prob. 4SWU Ch. 9.3 - Prob. 5SWU Ch. 9.3 - Prob. 6SWU Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 13E Ch. 9.3 - Using Two Methods In Exercises 13-16, find the...Ch. 9.3 - Prob. 15E 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 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 27E Ch. 9.3 - Prob. 28E Ch. 9.3 - Prob. 29E Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - Prob. 33E Ch. 9.3 - Prob. 34E Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Consumer Trends The number of coupons x used by a...Ch. 9.3 - Prob. 38E Ch. 9.3 - Prob. 39E Ch. 9.3 - Prob. 40E Ch. 9.3 - Transportation The arrival time t (in minutes) of...Ch. 9.3 - Prob. 42E Ch. 9.3 - Prob. 43E Ch. 9.3 - Prob. 44E Ch. 9.3 - Prob. 45E 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 - Prob. 48E Ch. 9.3 - Demand The daily demand x for water (in millions...Ch. 9.3 - Prob. 50E Ch. 9.3 - Prob. 54E Ch. 9.3 - Prob. 55E Ch. 9.3 - Education For high school graduates from 2012...Ch. 9.3 - Prob. 57E Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - Prob. 7RE Ch. 9 - Prob. 8RE Ch. 9 - Prob. 9RE Ch. 9 - Prob. 10RE Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - Prob. 14RE Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Revenue A publishing company introduces a new...Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - 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Knowledge Booster

To graph: The probability density function f ( x ) = 1 32 x over the interval [ 0 , 8 ] and calculate the probabilities (a) P ( 0 &lt; x &lt; 3 ) (b) P ( x = 7 ) (c) P ( 4 &lt; x &lt; 6 ) (d) P ( x ≥ 6 ) .

To graph: The probability density function f(x)=132x over the interval [0,8] and calculate the probabilities (a) P(0<x<3) (b) P(x=7) (c) P(4<x<6) (d) P(x≥6).

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Chapter 9 Solutions

To graph: The probability density function f ( x ) = 1 32 x over the interval [ 0 , 8 ] and calculate the probabilities (a) P ( 0 < x < 3 ) (b) P ( x = 7 ) (c) P ( 4 < x < 6 ) (d) P ( x ≥ 6 ) .