Question

3. Suppose that waiting times in a medical office are continuously and uniformly dis- tributed between 3 minutes and 12 minutes. (a) What is the probability of waiting less than 8 minutes? (b) What is the probability of waiting exactly 6 minutes? (c) What is the standard deviation of the waiting time?

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Answer #1

for uniform distribution ; parameter a =3 and b=12

a)

P(X<8)=(x-a)/(b-a) =(8-3)/(12-3)=5/9

b)

P(X=6) =0 (as for continuous distribution ; point probability is equal to 0)

c)

std deviation =(b-a)/sqrt(12)=(12-3)/sqrt(12)=2.598

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