Problem

In a recent year, the rate of U.S. home ownership…

06:57

Problem 10 Medium Difficulty

In a recent year, about 22% of Americans 18 years and older are single. What is the probability that in a random sample of 200 Americans 18 or older more than 30 are single?

Answer

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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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Lesek L.

July 13, 2021

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Watch More Solved Questions in Chapter 6

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Problem 10

Problem 11

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Video Transcript

Okay, this is for problem number 10. We have n equals 500 and we have p equals 56%. When you convert that to decimal, it's 0.56 Okay, Our standard deviation is end times P. So 500 times 5000.56 it's gonna give us 280. Okay. Our standard deviation is N P. Q. We already said NP was to 80 and cue is just one minus p, and that equals 11.10 Okay, around to one decimal, two decimal places if you need to. And we want to find the probability that X is greater than or equal to 250. Now we go to the table for for our continuity correction factor. Okay, When it's greater than or equal to, you have to subtract 0.5 and remove the equal sign. All right, so this becomes the probability that X is greater than to 49.5. Okay, you just you just subtract 0.5 from 2 50 and remove the equal sign. So that's gonna be our new X value. When we find the Z score. So Z equals X, which is to 49.5, minus the mean, which is to 80 divided by the standard deviation. Okay. And that is going to give us negative 2.75 All right, round to two decimal places, if you need to. You have to look up negative. 2.75 on the Z score table. OK? And when you do that, you will get a value of point 0030 Okay, now, that's the probability that X is less than 2 49.5 but we need it for greater than Okay. So in order to do that, you just subtract this value from one. Okay, So do one minus 0.30 Okay. And that gives us point 9970 All right. And to convert that to percentage, just move the decimal place over two places, so we get 99 0.70%

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