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In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of $n$ and $p ?$(a) $n=10, p=0.5$(b) $n=40, p=0.88$(c) $n=100, p=0.2$(d) $n=100, p=0.99$(c) $n=1000, p=0.003$

(c) $n=100, p=0.2$

Intro Stats / AP Statistics

Chapter 6

Random Variables

Section 3

Binomial and Geometric Random Variables

Descriptive Statistics

Probability Topics

Discrete Random Variables

Continuous Random Variables

The Normal Distribution

The Central limit Theorem

Missouri State University

Oregon State University

University of St. Thomas

Idaho State University

Lectures

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02:20

"In which of the fol…

03:56

Which of the following is …

04:27

Assume that x is a binomia…

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For which of the binomial …

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Which of the following val…

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When selecting a random sa…

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In which of the following …

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Check each binomial distri…

all right In this problem, we have thes binomial distributions, and we're tryingto figure out which of the cases we could approximate with normal distribution. So I read, I wrote down all the cases and then remember that to check for normal, that's just really means to check two things and that is, in p greater than or equal to 10 and is in Q or one minus p greater than equal a 10. That's where you need a check. So he's gonna go through these one by one. And actually, let's just make this a little easier, at least for me. I like to have things organized lists. I'm gonna make a table. We'll make this in P this in queue and I feel at my table, Um, nicely. So 1st 1 this also, by the way, I know it's my writing is not great. Sometimes that is supposed to be a 10.5 point five, while that's barely better, but a little bit better. So half of 10 is five and then one minus half is also half side. Make five also notice. These are gonna be complementary, because if the problem of probability of succeeding is one thing that I respect, probably failing to be the complimentary amount. So seeing equals 40 Siamese calculator just faster that way. 0.88 times, perhaps four oh, zero 35.2 and then poor 0.8. They're complimentary, and then 100 times 1000.2 is 20 and then that means that they're about the compliment. Amount would be 80 100 times 99.9 is 99. But that makes confident around one and 1000 times 10000.3 is three. And that makes the Compliment 997. And as we see here, the only one where both the left and right calm are greater than or equal to 10 would be. See, so see is the answer.

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