Question

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 0.04? (Round your answer to two decimal places.) cfs Need Help? Read It Talk to a Tutor Submit Answer

Answer 1

Girn, 0 а mean 100 CFS The operator of Pumping station has an oppassusretdy exponential distribution with a) Probability that demand will exceed 250cf8 :- P(Y > 250) 1- P(y2 250) - f(y) dy 250 -1/100 dy 100 O

دموع (ه) و -= ( 9 950 ۱۰ ( (%0) 1- [ « (1) 1%) (% 0كو ) . (2.5) +ا (0.583 ۱+ (-۵ ۰۹t79) the probability that exceed 250Cfs is "0.0821' | 0،082 = (250<۶)P/'۔

b) what handonly water - Pumping capacity :- the probability Giren that x demend will exceed capacity on a selected day is only 0.04 -) Pſy>c) -0.04 1-P(ycc) = 0.04 -9/00 e 10o 0 -0.04 1 + Jo = 0.04 the c*60 (-y) [e-9600] +(2-400-8600] it [eehoo e 0.04 1 + -0.04 y+ ég 400 -X = 0.04 [:eº é Yoo -0.04 - 100 in (0.04) -3-2189 100 to C- 321.89 = 43.2189 (100) .. C-321.89 - what peomping water pumping capacity - 327.89 cps