How long does it take to download a 2-hours HD movie to an iPad? According to Ap

Question

How long does it take to download a 2-hours HD movie to an iPad? According to Apple’s technicalsupport site [https://support.apple.com/en-us/HT201587], downloading a 2-hours HD movie using a 10Mbits/s broadband connection should take 42 to 60 minutes (as of 26 January 2016). If download times aredistributed continuously and uniformly between 42 and 60 minutes,

a. determine the probability the download time is at least 57 minutes.

b. determine the expected download time.

c. determine the standard deviation of download times.

d. determine the probability a download time is within one standard deviation of the expected downloadtime.

Please show work!

Explanation / Answer

this is a uniform distribution where a =42 and b=60 minutes

hence f(x) =1/(60-42) =1/18

a) probability the download time is at least 57 minutes =P(X>=57) =(60-57)/(60-42) =3/18=1/6

b) expected download time =(a+b)/2 =(42+60)/2 =51

c)std deviation =(b-a)/(12)1/2 =5.196

d)one std deviation away values =mean +/- std deviation =45.80 and 56.20

hence P(45.80<X<56.20) =(56.20-42)/(60-42) -(45.80-42)/(60-42) =0.7887 -0.2113 =0.5774

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