Suppose the download time of a smart phone app is uniformly

Suppose the download time of a smart phone app is uniformly distributed between 29 and 69 seconds. A. What is the probability that the download time will be less than 34 seconds? B. What is the probability that the download time will be less than 38 seconds? C. What is the probability that the download time will be between 38 and 48 seconds? D. What are the mean and standard deviation of the download times?

Solution

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )

f(x) = 1/(b-a) = 1 / (69-29) = 1 / 40 = 0.025

a)
P(X < 34) = (34-29) * f(x)
= 5*0.025
= 0.125

b)
P(X < 38) = (38-29) * f(x)
= 9*0.025
= 0.225

c)
P(38 < X < 48) = (48-38) * f(x)
= 10*0.025
= 0.25
d)
Mean = a + b / 2 = 49
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 11.547