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 theprobability density function for x is given by the following function.1f(x) =50 x, for 0≤x≤ 10Find P(2 ≤x≤ 9), the probability that the dart lands in [2,9].How is the probability that the dart lands in [2,9] found?O A. Evaluate the expression150x over the limits 2 and 9, then subtract.1O B. Integratex twice, then evaluate the integral over the limits 2 and 9.501O C. Evaluate the expressionx over the limits 2 and 9, then add.501O D. Integrate50x, then evaluate the integral over the limits 2 and 9.P(2≤x≤9)=(Type an integer or a simplified fraction.)

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Answered: A dart is thrown at a number line in…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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In a study of intelligence, the time (in seconds) for a laboratory animal to reach a reward in a maze was found to have a probability density function f(t) = 8 t 2 , t ≥ 8 where 8 seconds is the minimum time to traverse the maze. (a) Find the probability that an animal chosen at random takes between 28 and 56 seconds. (b) Find the probability that an animal chosen at random takes more than 28 seconds given that it took less than 56 seconds.

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