Question

Gio is pursuing a major in computer science. He notices a memory chip containing 2¹² = 4,096 bits is full of data. The data seems to be generated, bit-by-bit, at random, with 0’s and 1’s equally likely, and the bits are stored independently. If each bit is equally likely to be a 0 or 1, estimate the probability that there are actually 2,140 or more 1’s stored on the memory chip. Hint, use the normal approximation with a continuity correction.

Answer 1

This is binomially distributed with p=0.5 and n=4096

Expectation = np = 2048

Variance = np(1 - p) = 1024

Standard deviation = 32

With continuity correction z value for 2140, z= (2139.5 -2048)/32 = 2.86

The required probability

P( x ≥ 2140) = P( z > 2.86)

=0.0021

Excel function used: =1-NORM.S.DIST(2.86,TRUE)

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