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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?

0.9893

Intro Stats / AP Statistics

Chapter 6

The Normal Distribution

Section 4

The Normal Approximation to the Binomial Distribution

Probability Topics

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Lectures

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03:55

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In 2011, 12% of Americans …

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A. NO CHANGEB. Not so …

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00:34

Okay, so these are the three formulas will be using for the mean it's end times p for the standard deviation. It's the square root of N. P. Q. And for the Z score, it's X minus the mean divided by the standard deviation. Okay, we need this table for the continuity correction factor. Yeah, so on number nine, we have p equals 22% which is 220.22 And we have n equals 200. All right, so for our mean, it's just end times p. So 200 times 2000.22 is going to give us 44. Our standard deviation is the square root of end times P, which is 44 times Q, which is one minus p. All right, on the calculator, that's going to give us 5.86 Just round to two decimals, if you need to. All right. And we want to find the probability that X is greater than 30. Okay. And for our continuity correction, as you can see right here, you have to add 0.5. Okay, so we're gonna add 0.5 to 30 and we want to find the probability that X is greater than 30.5. All right, so that 30.5 is gonna be our new X value. So for the Z score for the Z score formula is X minus the mean, which is 44 divided by the standard deviation, which is 5.86 Okay, now this will give us negative 2.30 Okay, around 22 desperate places if you need to. And when you look up this Z score on the table, you should get 0.107 Okay, now, that's the probability that X is less than 30.5. Okay, So in order to find greater than 30.5, we have to subtract that value that we just got from one. So one minus 0.107 is gonna give us 0.9893 And to convert that to decimal, you just move the desperate place over two places. So that's 98.93 percent. Yeah,

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