Explanation Given Information: The probability density function f ( x ) = 1 50 ( 10 − x ) over the interval [ 0 , 10 ] . Graph: Consider the provided probability density function. f ( x ) = 1 50 ( 10 − 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 50 ( 10 − 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 = 0.5 Y s c l = 0.1 Step 4: Press the [GRAPH] key. The graph of the function f ( x ) = 1 50 ( 10 − x ) is obtained as, Now, calculate the probabilities. Consider the provided probability density function f ( x ) = 1 50 ( 10 − 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 50 ( 10 − x ) d x Use the formula ∫ x n d x = x n + 1 n + 1 and integrate. ∫ c d 1 50 ( 10 − x ) d x = 1 50 ( 10 x − x 2 2 ) c d (a) To calculate P ( 0 < x < 2 ) , use the Fundamental theorem ∫ a b f ( x ) d x = F ( b ) − F ( a ) and apply the limits on 1 50 ( 10 x − x 2 2 ) c d . 1 50 ( 10 x − x 2 2 ) 0 2 = 1 50 ( 10 ( 2 ) − 2 2 2 − 0 ) = 1 50 ( 20 − 2 ) = 18 50 = 9 25 Thus, the probability of P ( 0 < x < 2 ) is 9 25 . (b) To calculate P ( x ≥ 7 ) , use the Fundamental theorem ∫ a b f ( x ) d x = F ( b ) − F ( a ) and apply the limits on 1 50 ( 10 x − x 2 2 ) c d . 1 50 ( 10 x − x 2 2 ) 7 10 = 1 50 ( ( 10 ( 10 ) − 10 2 2 ) − ( 10 ( 7 ) − 7 2 2 ) ) = 1 50 ( ( 100 − 50 ) − ( 70 − 49 2 ) ) = 1 50 ( 50 − 70 + 49 2 ) = 1 50 ( − 20 + 49 2 ) Simplify

Calculus: An Applied Approach (Providence College: MTH 109)

9th Edition

ISBN: 9781285142616

Author: Ron Larson

Publisher: CENGAGE C

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Chapter 9, Problem 33RE

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To graph: The probability density function f(x)=150(10−x) over the interval [0,10] and calculate the probabilities (a) P(0<x<2) (b) P(x≥7), (c) P(x≤5),(d) P(8<x<9).

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Chapter 9, Problem 32RE

Chapter 9, Problem 34RE

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Chapter 9 Solutions

Calculus: An Applied Approach (Providence College: MTH 109)

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 - 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To graph: The probability density function f ( x ) = 1 50 ( 10 − x ) over the interval [ 0 , 10 ] and calculate the probabilities (a) P ( 0 < x < 2 ) (b) P ( x ≥ 7 ) , (c) P ( x ≤ 5 ) ,(d) P ( 8 < x < 9 ) .

Solution Summary: The author explains how to graph the probability density function using the ti-83 graphing calculator.

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To graph: The probability density function f(x)=150(10−x) over the interval [0,10] and calculate the probabilities (a) P(0<x<2) (b) P(x≥7), (c) P(x≤5),(d) P(8<x<9).

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Chapter 9 Solutions

To graph: The probability density function f ( x ) = 1 50 ( 10 − x ) over the interval [ 0 , 10 ] and calculate the probabilities (a) P ( 0 &lt; x &lt; 2 ) (b) P ( x ≥ 7 ) , (c) P ( x ≤ 5 ) ,(d) P ( 8 &lt; x &lt; 9 ) .

Solution Summary: The author explains how to graph the probability density function using the ti-83 graphing calculator.

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To graph: The probability density function f(x)=150(10−x) over the interval [0,10] and calculate the probabilities (a) P(0<x<2) (b) P(x≥7), (c) P(x≤5),(d) P(8<x<9).

Want to see the full answer?

Chapter 9 Solutions

To graph: The probability density function f ( x ) = 1 50 ( 10 − x ) over the interval [ 0 , 10 ] and calculate the probabilities (a) P ( 0 < x < 2 ) (b) P ( x ≥ 7 ) , (c) P ( x ≤ 5 ) ,(d) P ( 8 < x < 9 ) .