The document discusses the probability of bit errors in a binary message of length n sent over a noisy channel, specifically focusing on approximating the likelihood of experiencing between 10 and 20 errors. It suggests the use of a continuity correction and normal approximation, expressing the result in terms of the cumulative distribution function (cdf) of the standard normal distribution.

1. 7. [2.5] A binary (0s and 1s) message of length n bits is sent over a noisy channel. The
probability that any particular bit is received incorrectly is p . Use a continuity correction and a
normal approximation, to approximate the probability that between 10 and 20 errors occur
(including 10 and 20). Express your answer in terms of , the cdf of the Standard Normal
distribution.