Concept explainers
Life Span of A Plant Species The life span of a certain plant species (in days) is described by the probability density function
a. Find the probability that a plant of this species will live for 100 days or less.
b. Find the probability that a plant of this species will live more than 120 days.
c. Find the probability that a plant of this species will live more than 60 days but less than 140 days.
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Chapter 7 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
- 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.arrow_forwardDecay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forwardFinding Probabilities in Uniform Distributions The time it takes me to wash the dishes is uniformly distributed between 9 minutes and 15 minutes. The probability density function is f(x)=16f(x)=16.What is the probability that washing dishes tonight will take me between 12 and 13 minutes?Give your answer accurate to two decimal places.arrow_forward
- In a manufacturing process involving several machines, the average down time t (in hours) for a machine that needs repair has the probability density function given below. f(t) = 0.5e−0.5t t ≥ 0 (a) Find the probability that a failed machine's down time is 3 hours or more. (Round your answer to three decimal places.) (b) Find the probability that a failed machine's down time is 11 hours or more. (Round your answer to four decimal places.)arrow_forwardLet X be the number of minutes that it takes a random selected student to solve a mathematical problem. The probability density function of X is: 1) Find the probability that a student takes less than 1.5 minutes to solve themathematical problem.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage