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According to the U.S. Census, 67.5% of the U.S. population were born in their state of residence. In a random sample of 200 Americans, what is the probability that fewer than 125 were born in their state of residence?

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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According to the U.S. Cens…

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Home Ownership In a recent…

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According to a 2007 Americ…

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In a recent year, it was e…

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College students often mak…

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In a survey of 500 randoml…

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04:55

A 2010 study conducted by …

okay. For number 20 we have an equals 200. We have p equals 67.5% which is 0.675 All right, the mean is just n times P. And that's gonna equal 135. The standard deviation. It's a square root of end times P times Q, which is just one minus p. And that's going to give us 6.62 rounded to two gas mus. All right, we want to find the probability that X is less than 1 25 and going to our continuity conversion short when X is less than a number, you subtract 0.5. So 1 25 minus 0.5 gives us 1 24.5 That's gonna be our new X value. And when we calculate the Z score, you do X minus the mean divided by the standard deviation. And you should yet negative 1.59 Okay? Yeah, When you look up that value on the Z score table, you should get point 0559 And that gives us the probability that X is less than 1 24.5 That's exactly what we want. So just convert this 2% move the decimal two places and you should get 5.59% and that's for number 20.

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