2. [-/5 Points]DETAILSDEVORESTAT9 4.4.060.Need Help?MY NOTESLet X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distributionwith parameter > = 0.01342.(a) What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? (Round your answers to four decimal places.)at most 100 mat most 200 mbetween 100 and 200 m(c) What is the value of the median distance? (Round your answer to two decimal places.)mASK YOUR TEACHER(b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.)Read ItPRACTICE ANOTHER

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Answered: /5 Points] DETAILS DEVORESTAT9 4.4.060.…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that during rainy season on a tropical island the length of theshower has an exponential distribution, with parameter λ = 2, time beingmeasured in minutes. What is the probability that a shower will last morethan three minutes? If a shower has already lasted for 2 minutes, what is theprobability that it will last for at least one more minute?
The Rivera Family has put up a small business, which sells cakes and pastries. It was observed that the time (in minutes) between order placements follows an exponential distribution with a rate parameter of 1/17. After receiving the first order, what is the probability that the family will have to wait: more than 23 minutes for the next order? at most 14.37 minutes for the next order? between 19.05 and 25.40 minutes for the next order?
Suppose that the first Section of Applied Stat class ends at 13:20 and the second starts at 13:30 with ten minutes break. Professor, who teaches both sections, wants to go to bathroom during the break. Suppose that the time that takes for professor to go to bathroom and come back to the classroom has an exponential distribution with the mean of 6.7 minutes. Find the probability that the professor will be late for class for less than 3 minutes (round to 3 decimal places).
The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). b) What water-pumping capacity should the station maintain during early afternoons so that the probability that demand will be below the capacity on a randomly selected day is 0.995? c) Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?
Suppose that, at a newsstand, customers who buy a newspaper or magazine do so with an average of 1.6 customers per minute. If you are interested in modeling the waiting time until the arrival of the next customer. j) The probability that the next customer will take one standard deviation around the expected value.
The operator of a pumping station has observed that demand for waterduring early afternoon hours has an approximately exponential distribution with mean 1000cfs (cubic feet per second).a) Find the probability that the demand will exceed 700 cfs during the early afternoonon a randomly selected day.b) What water-pumping capacity should the station maintain during early afternoons sothat the probability that demand will be below the capacity on a randomly selectedday is 0.995?c) Of the three randomly selected afternoons, what is the probability that on at least twoafternoons the demand will exceed 700 cfs? 2. Let Y1 and Y2 be random variables with joint density functionf(y1, y2) = (6/7(y^2+y1y2/2) 0 < y1 < 1, 0 < y2 < 2,0, elsewherea) Find marginal density functions. Are Y1 and Y2 independent?b) Find P(0 < Y1 < 0.3, −2 < Y2 < 1).c) Find P(0.6 < Y1 < 1|0 < Y2 < 1). 3.The joint density function of Y1 and Y2 is given byf(y1, y2) = (y1 + y2), 0 <…
Suppose that the waiting time to see the doctor at a clinic is exponentially distributed with mean 50 minutes. The consultation time with the doctor is uniformly distributed between 10 and 20 minutes. If both these variables are independent, what is the probability that the total time spent at the clinic is less than one hour?
The lifetime of an aquatic insect has an exponential disribution with parameter θ = 10 hrs. (i) What is the probability that an aquatic insect lives longer than 12 hrs? (ii) What is the median of this distribution? (50% live less time and 50% live longer) (iii) Assume the lifetimes of these insects are independent of each other. What is the probability that at least 35 of the next 100 insects live longer than 12 hrs?

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