Question #2 (10 points): The file transfer speed from a server to a computer loc
ID: 3066797 • Letter: Q
Question
Question #2 (10 points): The file transfer speed from a server to a computer
located in a household is late on a weekday evening is normally distributed
with a mean of 60 megabits per second and a standard deviation of 4
megabits per second. (a) What is the probability that a file will transfer at a
speed of 70 megabits per second or more? (b) What is the probability that a
file will transfer at a speed of less than 58 megabits per second? (c) What is
the probability that a file will transfer at a speed of greater than 50 megabits
per second and less than 69 megabits per second? (d) If the file is 100
megabyte, what is the average time it will take to transfer the file (assume 8
bits/byte)?
Explanation / Answer
P(X < A) = P(Z < (A - mean)/standard deviation)
Mean = 60 megabits per second
Standard deviation = 4 megabits per second
a) P(X > 70) = 1 - P(X < 70)
= 1 - P(Z < (70-60)/4
= 1 - P(Z < 2.5)
= 1 - 0.9938
= 0.0062
b) P(X < 58) = P(Z < (58 - 60)/4)
= P(Z < -0.5)
= 0.3085
c) P(50 > X > 69) = P(X < 69) - P(X < 50)
= P(Z < (69-60)/4) - P(Z < (50-60)/4)
= P(Z < 2.25) - P(Z < -2)
= 0.9878 - 0.0228
= 0.9650
d) Speed is 60megabits per second = 60/8 = 7.5 megabytes per second
Average time it will take tot transfer a 100 megabyte file = 100/7.5 = 13.33 seconds