Suppose you sample on value from a uniform distribution with

Suppose you sample on value from a uniform distribution with a = 0 and b = 50.

A. What is the probability that the value will be between 37 and 40?

B. What is the probability that the value will be between 6 and 22?

C. What is the mean?

D. What is the standard deviation?

Solution

a)

P(37<x<40) = (40-37)/(50-0) = 0.06 [ANSWER]

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b)

P(6<x<22) = (22-6)/(50-0) = 0.32 [ANSWER]

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c)

For a uniform disitrbution from (a,b),

Mean = (a+b)/2 = (50+0)/2 = 25 [ANSWER]

d)

standard deviation = sqrt((b-a)^2/12) = sqrt((50-0)^2/12) = 14.43375673 [ANSWER]