Suppose that the time it takes a user to connect to the internet has a continuou

Question

Suppose that the time it takes a user to connect to the internet has a continuous uniform distribution with a shortest possible connection time of .5 minutes and maximum connection time of 4.25 minutes. If this particular user attempts to connect to the internet today, find the probability that she connects in          a) at most 3 minutes___________, between 2 and 2.5 minutes_________________.            The mean and standard deviation of the connection times are mean=_____________ and standard deviation=________________.

Explanation / Answer

X ~ U (0.5 , 4.25)

a) P(X < 3) = (3 - 0.5) / (4.25 - 0.5) = 0.6667

b) P(2 < X < 2.5) = (2.5 - 2) / (4.25 - 0.5) = 0.1333

c) Mean = (0.5 + 4.25) / 2 = 2.375

d) standard deviation = (4.25 - 0.5) / sqrt(12) = 1.08

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