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A dart is thrown at a number line in such a way that it always lands in the interval (0,10J. Let x represent the number that the dart hits. Suppose that the probability density function for x is given by the following function. f(x) = 50 X, for 0sxs 10 Find P(3sxs7), the probability that the dart lands in [3,7].

A dart is thrown at a number line in such a way that it always lands in the interval (0,10J. Let x represent the number that the dart hits. Suppose that the probability density function for x is given by the following function. f(x) = 50 X, for 0sxs 10 Find P(3sxs7), the probability that the dart lands in [3,7].

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 4CR
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A dart is thrown at a number line in such a way that it always lands in the interval [0,10]. Let x represent the number that the dart hits. Suppose that the probability density function for x is given by the following function. 1 f(x) = -x, for 0 <x<10 50 Find P(3<x<7), the probability that the dart lands in [3,7].
Transcribed Image Text:A dart is thrown at a number line in such a way that it always lands in the interval [0,10]. Let x represent the number that the dart hits. Suppose that the probability density function for x is given by the following function. 1 f(x) = -x, for 0 <x<10 50 Find P(3<x<7), the probability that the dart lands in [3,7].
How is the probability that the dart lands in [3,7] found? 1 O A. Evaluate the expression -x over the limits 3 and 7, then subtract. 50 1 O B. Evaluate the expression x over the limits 3 and 7, then add. 50 OC. Integrate 1 x, then evaluate the integral over the limits 3 and 7. 50 1 O D. Integrate x twice, then evaluate the integral over the limits 3 and 7. 50 P(3<xs7) = (Type an integer or a simplified fraction.)
Transcribed Image Text:How is the probability that the dart lands in [3,7] found? 1 O A. Evaluate the expression -x over the limits 3 and 7, then subtract. 50 1 O B. Evaluate the expression x over the limits 3 and 7, then add. 50 OC. Integrate 1 x, then evaluate the integral over the limits 3 and 7. 50 1 O D. Integrate x twice, then evaluate the integral over the limits 3 and 7. 50 P(3<xs7) = (Type an integer or a simplified fraction.)
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