Question

How long does it take to download a two0hour HD movie from the itunes store? According to Apple's technical support site, support.apple.com/en-us/HT201587, downloading such a movie using a 15 Mbit/s broadband connection should take 29-43 minutes. Assume that the download times are uniformly distributed between 29 and 43 minutes. If you download a two hour movie, what is the probability that the download time will be:

A. less than 30 minutes?

B. more than 36 minutes?

C. between 30 and 40 minutes?

D. What are the mean and standard deviation of the download times?

Answer 1

Solution :

Given that,

a =29

b = 43

(a) P(x < c) = (c - a) / (b - a)

P(x <30) = (30 - 29) / (43 - 29) = 0.0714

Probability = 0.07

(b)P(x > c) = (b - c) / (b - a)

P(x > 36) = (43 - 36) / (43 - 29) = 0.5

Probability = 0.5

(c)P(c < x < d) = (d - c) / (b - a)

P(30 < x < 40) = (40 - 30) / (43 - 29) = 0.7143

Probability = 0.71

(d)

mean = (a + b) / 2 = (29 + 43) / 2 = 36

(e)

standard deviation =  (b - a)² / 12 = (43 - 29)² / 12 = 4.0415 rounded = 4.04