7/E 322: Final Dr. Eunhye Song (15 points) In a communication system each data p

Question

7/E 322: Final Dr. Eunhye Song (15 points) In a communication system each data packet consists of 1000 bits. Note that bits are countable (integer-valued) and arriving one by one. Due to the noise, each bit may be received corrupted with probability 0.1. It is assumed bit corruption occurs independently (a) Find the probability that there are more than 120 errors in a certain data packet using a normal approximation. Use the closest critical value in the table. Do no interpolate. (b) If the third corrupted bit is detected within the first six received bits, then the syster is flagged for maintenance. What is the probability that the system is flagged? KEE FOUR DIGITS AFTER THE DECIMAL POINT

Explanation / Answer

p = 0.1

n = 1000

Mean = 0.1 * 1000 = 100

SD = sqrt( 100 * 0.9) = 9.49

a) z = (120 - 100)/9.49

z = 2.11

P(z > 2.11 ) = 0.0174

b) We have to find P(X = 3), supposing that when x = 3 immediately system will be flagged

P = 6C3 * 0.1^3 * 0.9^3

P = 0.0146

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