11. The digestion time in hours of a fixed amount of food is exponentially distributed with average1/a. What isthe probability that the food is digested in less than 30 minutes? In more than 60 minutes?45 minutes. Recall that p(t)ke-kt for t > 0 (in minutes), where ka =Between 35 and 55 minutes?

The exponential distribution is the continuous distribution which is defined for the time between…

Answered: The digestion time in hours of a fixed…

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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Let 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 distribution with parameter a = 0.01437. (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 100m at most 200m between 100 and 200 m (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.) (c) What is the value of the median distance? (Round your answer to two decimal places.)
The probability of a transistor failing between t = a months and t = b months is given by c ect dt. for some constant c. (a) If the probability of failure within the first six months is 10%, what is c? Round your answer to four decimal places. eTextbook and Media (b) Given the value of c in part (a), what is the probability the transistor fails within the second six months? Round your answer to the nearest integer.
The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 6 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement. Find the probability that the person retired after age 70. (Round your answer to four decimal places.) In a room of 1,000 people over age 82, how many do you expect will NOT have retired yet? (Round your answer to the nearest whole number.) ch5#4
a. b. Let X have a gamma distribution with a=2 and 3-2. What is P(X>2)? Let X have a log-normal distribution with u-3.5 and o=1.2. Find P(50
2 The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 250 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.02? (Round your answer to two decimal places.) cfs
The life X (in hours) of a battery in constant use is an arbitrary variable with exponential density. What is the probability that the battery will last more than 28 hours if the average life is 8 hours? (Give your answer to four decimal places.) P≈
Let 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 distribution with parameter å = 0.01417. (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 m at most 200 m between 100 and 200 m (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.) (c) What is the value of the median distance? (Round your answer to two decimal places.)

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