Problem

Recall that for use of a normal distribution as a…

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Problem 22 Hard Difficulty

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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Intro Stats / AP Statistics

Elementary Statistics a Step by Step Approach

Chapter 6

The Normal Distribution

Section 4

The Normal Approximation to the Binomial Distribution

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Jared K.

December 1, 2020

5) Given each probability of a success, what would be the minimum sample size needed to use the normal approximation? a) p= 0.3 ____________________ b) p= 0.85 ____________________ c) p= 0.5

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Video Transcript

okay. For number 22 we have n equals 350 and we have p equals 35%. All right, so our mean it's just end times p, and that's going to give us 1 22.5 Our standard deviation is the square root of end times P times Q, which is just one minus p. And you should get 8.92 rounded to two decimal places. Okay, we want to know the probability that X is greater than or equal to 100 and going to our continuity conversion. You subtract 0.5 and remove the equal sign when X is greater than or equal to a number. Okay, so we subtract 0.5 from 100 which gives us 99.5 okay and remove the equal sign. So that's gonna be our new X value and Z score. It's X minus the mean divided by the standard deviation, and you should get negative 2.58 When you look up that value on the Z score table, you should get 0.0 zero 49 Okay, now, this is if X were less than 99.5. Since we want to know greater than we have to subtract this value from one. So one minus 0.49 gives us 0.9951 and converting that to decimal. You should get 99.51 percent. And they ask, Is this likely? Well, yeah, that's very likely. Okay, it's over 99% chance, so that's very likely to a car.

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