Assume that in a digital communication channel the number of

Assume that in a digital communication channel, the number of bits received in error can be modeled by a binomial random variable, and assume that the probability that a bit is received in error is 10^-5. If 16 million bits are transmitted, estimate the probability that 150 or fewer errors occur?

Hint: You need to choose the right approximation

Solution

p = 0.00001

n = 16 x 10^6

P(n<=150) = ?

here,

m = n*p = 16 * 10^6 * 10^-5 = 160

sd = sqrt(npq) = sqrt(16*10^6 * 10^-5 * 0.99999) = 12.64

P(n<=150) = P( z < (150-160)/12.64) = P(z<-0.79) = 0.2148