I have doubts doing this exercise

II. (25%) A T1 line is a high speed digital telecommunications circuit. A T1 line uses a technique called framing for keeping the line synchronized by constantly transmitting a unique framing pattern using a special framing bit. Each frame has 1 framing bit and 24 channels of 8 payload bits each. Each channel carries 64,000 bits per second or 64 Kbps per channel. Consequently, a T1 line has a payload capacity of (24 channels)x(64 Kbps per channel) =1536 Kbps or 1.536 Mbps. Assume that UPR-Mayaguez has three T1 Lines available. On the other hand, assume that X = the bandwidth demand of the Engineering College at UPRM is a random variable with the following pdf (for x > 0, x in Kbps): f(x) = (1/500) (x/1000) exp[ -(x/1000)2 ], x > 0 1] (6%) The standard deviation (in Kbps) of the bandwidth demanded by the Engineering College is A) 214.60 B) 463.25 C) 367.81 D) Not defined e) None of these 2] (6%) The median (in Kbps) of the bandwidth demanded by the Engineering College is A) 787.23 B) 708.6 C) 732.55 D) 808.1 e) None of these 3] (6%) Assume that the Engineering College needs to request a certain number of dedicated channels of the T1 lines to the Administration of the UPRM. A technician estimate the number of channels to request by dividing the mean bandwidth demand by the bandwidth of a single channel (64 Kbps) and rounding up. Compute the probability that the bandwidth demand exceeds the total bandwidth requested by the technician. A) 0.4998 B) 0.5519 C) 0.4481 D) 0.50046 e) None of these 4] (6%) The Dean of the College of Engineering wants that the probability that the bandwidth demand exceeds the total bandwidth available be at most 5%. What is the minimum number of channels of the T1 Lines that the technician must request to satisfy the Dean's specification? A) 1731 B) 24 C) 27 28 e) None of these