1. [6 points] A lab network consisting of 10 computers was attacked by a compute

Question

1. [6 points] A lab network consisting of 10 computers was attacked by a computer virus. This virus enters each computer with probability 0.25, independently of other computers. Use th MegaStat output to answer the following questions. 10 n 0.25 p (a) Find the probability that it entered 6 computers. cumulative XPRO probability 0 0.05631 005631 0.18771 .24403 2 0.28157 0.52559 3 0.25028 0.77588 40.14600 0.92187 5 0.05840 0.98027 0.01622 0.99649 (b) Find the probability that it entered at least 5 computers. 7 0.00309 0.99958 8 0.00039 0.90997 9 0.00003 1.00000 10 0.00000 1.00000 (e) Find the probability that it entered 3 to 7 computers (inclusive). (d) Find the mean and standard deviation of the number of infected computers.

Explanation / Answer

A) P(X = 6) = 0.01622

B) P(X > 5) = 1 - P(X < 5) = 1 - F(4) = 1 - 0.92187 = 0.07183

C) P(3 < X < 7) = P(X < 7) - P(X < 3) = F(7) - F(2) = 0.99958 - 0.52559 = 0.47399

D) Mean = n * p = 10 * 0.25 = 2.5 or 3 (approximately)

Standard deviation = sqrt(n * p * (1-p)) = sqrt(10 * 0.25 * 0.75) = 1.37 or 1 (approximately)

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