How long does it take to download a two-hour movie from the iTunes store? Accord

Question

How long does it take to download a two-hour movie from the iTunes store? According to Apple’s technical support site, downloading such a movie using a 5 Mbit/s broadband connection should take 18 to 24 minutes. Assume that the download times are uniformly distributed between 18 to 24 minutes. Also assume you use a 5 Mbit/s broadband connection.

If you download a two-hour movie, what is the probability that the download time will be less than 19 minutes?

Refer back to the movie download information. If you download a two-hour movie, what is the probability that the download time will be between 15 to 21 minutes?

Refer back to the movie download information. If you download a two-hour movie, what is the probability that the download time will be exactly 21 minutes?

Explanation / Answer

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 / (24-18) = 1 / 6 = 0.1667
Mean = a + b / 2 = 21
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 1.732
a.
P(X < 19) = (19-18) * f(x)
= 1*0.1667
= 0.167

b.
To find P(a < X < b) =( b - a ) * f(x)
P(15 < X < 21) = (21-15) * f(x)
= 6*0.1667
= 1

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