Your answer is correct. 2 The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x) = Determine the following (round all of your answers to 3 decimal places): for for x > 1. (a) P(X < 4) 0.938 (b) P(X>7) 0.020 (c) P(3 < X < 7) 0.091 (d) P(X < 3 or X > 7) 0.909 (e) Determine x such that P(X < x) = 0.90. 3.162 eTextbook and Media

Your answer is correct. 2 The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x) = Determine the following (round all of your answers to 3 decimal places): for for x > 1. (a) P(X < 4) 0.938 (b) P(X>7) 0.020 (c) P(3 < X < 7) 0.091 (d) P(X < 3 or X > 7) 0.909 (e) Determine x such that P(X < x) = 0.90. 3.162 eTextbook and Media

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 12E: Average Traffic Spacing The headway h is the average time between vehicles. On a highway carrying an...

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Average Traffic Spacing The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per flour, the probability P that the headway is at least t seconds is given by P=0.87t. a. What is the limiting value of P? Explain what this means in practical terms. b. The headway h can be calculated as the quotient of the spacing f, in feet, which is the average distance between vehicles, and the average speed v, in feet per second, of traffic. Thus, the probability that spacing is at least f feet is the same as the probability that the headway is at least f/v seconds. Use function composition to find a formula for the probability Q that the spacing is at least f feet. Note: Your formula will involve both f and v. c. If the average speed is 88 feet per second 60 miles per hour, what is the probability that the spacing between two vehicles is at least 40 feet?
A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.
Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 stores. Using a new system, which allows the supermarket to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 28 seconds. (a)Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket. f(x) = x ≥ 0 elsewhere (b) What is the probability that a customer will have to wait between 30 and 45 seconds? (Round your answer to four decimal places.) (c) What is the probability that a customer will have to wait more than 2 minutes? (Round your answer to four decimal places.)
Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 stores. Using a new system, which allows the supermarket to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 23 seconds. (a) Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket. f(x) = , x ≥ 0 , elsewhere (b) What is the probability that a customer will have to wait between 30 and 45 seconds? (Round your answer to four decimal places.) (c) What is the probability that a customer will have to wait more than 2 minutes? (Round your answer to four decimal places.)
You pay 10 dollars to pick two numbers, with replacement, between 1 and 1000 at random. If the numbers are the same, you win 100 dollars. If not, you win nothing. IfXis the amount of money gain, find the probability density function forX.
Martian potatoes begin to sprout very quickly after planting. Suppose X is the number of days after planting until a Martian potato sprouts. Then X has the following probability density function: f(x)= 2/7e−x + 3/14e−x/2 + 1/14e−x/4 for 0 ≤ x ≤ ∞ and 0 otherwise. a)What is the probability that a Martian potato takes no more than 4 days to sprout? b) What is the probability that X >4? c) What is the probability that 2< X < 4? d) What is the expected value of X (E(X))? e) What is the expected value of X2 ? f) What is the variance of X? g) What is the standard deviation of X? h) What is the probability that X is more than 2 standard deviations above its expected value? i) What is the expected value of X4 ? j) What is the probability that X is within 1 standard deviation of its expected value? k) What is the probability that X = .6?