Problem 13 The daily amount of coffee, in liters per day, dispensed by the vendo

Question

Problem 13 The daily amount of coffee, in liters per day, dispensed by the vendor in the ElB building is a random variable, X, with between 7 and 10 liters dispensed in a uniformly distributed manner. Use the above data to determine: a. Probability that at most 8.8 liters will be dispensed. b. How many liters of coffee should the vendor expect to dispense in a given day? c. What range of coffee should the vendor order to be sure that he/she has about a 95% chance of meeting all the demand yet retaining little inventory?

Explanation / Answer

here for uniform distribution CDF =F(X<x)=(x-a)/(b-a) =(x-7)/(10-7)=(x-7)/3

a)hence probabilty that most 8.8 litre will be dispensed =P(8.8-7)/3=0.6

b)expected value =mean =(a+b)/2 =(7+10)/2 =8.5

c) for 0.95 =(X-7)/3

X=9.85

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