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Unformatted text preview: 905) ≈ 0.0567. The Gaussian approximation in this case is fairly accurate: numerical calculation, using the binomial distribution, yields that P {X − 50 ≥ 6} ≈ 0.0540.
(c) The Chebychev inequality implies that P {X − 50 ≥ 6} ≤
times larger than the value found in part (b). 2
σX
36 = 0.231, which is about four Example 3.6.10 A campus network engineer would like to estimate the fraction p of packets
going over the ﬁber optic link from the campus network to Bardeen Hall that are digital video disk
(DVD) packets. The engineer writes a script to examine n packets, counts the number X that are
DVD packets, and uses p = X to estimate p. The inspected packets are separated by hundreds of
ˆ
n
other packets, so it is reasonable to assume that each packet is a DVD packet with probability p,
independently of the other packets.
(a) Using the Gaussian approximation to the binomial distribution, ﬁnd an approximation to
P {p − p ≤ δ } as a function of p, n, and δ. Evaluate it for p = 0.5 and for p...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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