A number x is selected at random from the interval [4,20]. The probability density function for x is given by the following function. Find the probability that anumber selected is in the subinterval [5,17].f(x) = for 4 ≤x≤20.116'How is the probability that a number selected is in the subinterval [5,17] calculated?1ⒸA. Integratetwice, then evaluate the integral over the limits 5 and 17.161B. Evaluateover the limits 5 and 17, then add.161OC. Integratethen evaluate the integral over the limits 5 and 17.161O D. Evaluate over the limits 5 and 17, then subtract.16The probability is

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Answered: A number x is selected at random from…

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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A bottling company produces bottles of fruit juice that are filled, onaverage, with 32 ounces of juice. Due to random fluctuations in the machinery, the actual volume of juice is normally distributed with a standarddeviation of 0.4 oz. Let P be the probability of a bottle having less than31 oz. Express P as an integral of an appropriate density function andcompute its value numerically.
If the total nunber of hours spent by a student to study his/her module over one day is a continuous random variable X that has the density function *refer from attached* Find the probability that in one day, the student is studying a) less than 1 hr b) between 2 and 3hrs c) more than 3hrs
The driving time for an individual from his home to his work is uniformly distributed between 400 to 520 seconds. (a) Determine the probability density function. f(x) = , 400 ≤ x ≤ 520 0, elsewhere
Suppose the duration (in hours) of a certain valve is a random variableX with density function f(x) = 648x−4 for x > 6, and zero otherwise. What's the time expected life (in hours) of this valve?
There are 3 blue and 5 green marbles in a box. Balls are selcted at random, one after another without replacement, until a green ball is selected. Let X be a random variable whose value is the number of balls drawn. Find the density function of X.
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A sample (X1, ..., X10) is drawn from a distribution with a probability density function. The sum of all 10 observations equals 150.(a) Estimate θ by the method of moments.
It is known that the length of time X (in hours) it takes for pizza to be delivered by Domino’s Pizzza hasthe probability density function:f(x) = (12(x^2 − x^3) when 0 < x < 1, and 0 otherwise.a) Find the probability that it will take more than 20 minutes for a pizza to be delivered.b) Find the probability that it will take less than 40 minutes for a pizza to be delivered.c) If 10 independent deliveries are made on a particular day, what is the probability that exactly 7 of them took more than 20 minutes.
The random variable Z has a uniform distribution in the unit interval and the X is uniform on [z, z + 1]:• Draw the region of (X, Z) where their density function is defined.• What is the probability of 0.5 < X?• What is the expected value of X?• What is the probability of 0.5 < Z?• How you can interprept their correlation QUANTIATIVELY?
Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.
Suppose that the lifetime X (in hours) of a certain type of flashlight battery is a random variable on the interval 30 ≤ x ≤ 50 with density function f(x) = 1/20, 30 ≤ x ≤ 50. Find the probability that a battery selected at random will last at least 35 hours.
A random variable is called a power law random variable ifP(X > t) = max{1/(t^α), 1}for some α. What is the density of X? Compute the mean of X when α > 1. What happens if α < 1?

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