The mayor of a small town estimates that 35% of the...

Name: Problem 22, Chapter 6: Elementary Statistics a Step by Step Approach
Uploaded: 2020-07-27T19:16:03-08:00
Duration: 3 min 47 s
Channel: William Scherer
Description: The mayor of a small town estimates that 35% of the residents in the town favor the construction of a municipal parking lot. If there are 350 people at a town meeting, find the probability that at least 100 favor construction of the parking lot. Based on your answer, is it likely that 100 or more people would favor the parking lot?

The mayor of a small town estimates that 35% of the residents in the town favor the construction of a municipal parking lot. If there are 350 people at a town meeting, find the probability that at least 100 favor construction of the parking lot. Based on your answer, is it likely that 100 or more people would favor the parking lot?

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Key Concepts

Binomial Distribution

This concept refers to the probability distribution of the number of successes in a fixed number of independent trials, each with the same probability of success. It is crucial in scenarios where each trial results in a binary outcome (such as favoring or not favoring a proposal) and helps form the basis of calculations like finding the probability that at least a certain number of successes occur.

Normal Approximation to the Binomial

When the number of trials in a binomial distribution is large, it can be approximated by a normal distribution. This approximation simplifies calculations, especially when determining tail probabilities, and is based on the central limit theorem which justifies that the sum of many independent random variables tends toward a normal distribution.

Continuity Correction

This is an adjustment applied when a discrete distribution (like the binomial) is approximated using a continuous distribution (like the normal). The continuity correction improves the approximation by accounting for the fact that discrete outcomes are represented by continuous variables in the approximation process.

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