An interactive system at. Flybynight Airlines has 200...

Name: Problem 33, Chapter 3: Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)
Uploaded: 2022-04-08T02:35:14-08:00
Duration: 1 min 1 s
Channel: Nick Johnson
Description: An interactive system at. Flybynight Airlines has 200 workstations each connected by a local area network (LAN) to the local computer center. Each workstation independently has probability 0.05 of being signed on to the computer center. What is the probability that 20 or more of the workstations are signed on? Use the normal approximation if you can't make the exact calculation.

An interactive system at. Flybynight Airlines has 200 workstations each connected by a local area network (LAN) to the local computer center. Each workstation independently has probability 0.05 of being signed on to the computer center. What is the probability that 20 or more of the workstations are signed on? Use the normal approximation if you can't make the exact calculation.

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Key Concepts

Mean and Variance Calculation

For a binomial distribution, the mean is calculated as the product of the number of trials and the probability of success (np) while the variance is given by np(1-p). These parameters are essential when approximating the binomial distribution with a normal distribution.

Binomial Distribution

This concept involves modeling the number of successes in a fixed number of independent trials, where each trial has the same probability of success. It applies to situations where events occur with two outcomes (e.g., success or failure), and the overall count of successes is of interest.

Normal Approximation

When the number of trials is large and the success probability is moderate, the binomial distribution can be approximated by a normal distribution. This simplifies calculations by allowing the use of continuous probability methods in place of discrete ones.

Continuity Correction

When approximating a discrete distribution (like the binomial) with a continuous one (like the normal), a correction is often applied to improve accuracy. This involves adjusting the discrete value by 0.5 in the appropriate direction to account for the difference between discrete and continuous probability distributions.

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