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Check each binomial distribution to see whether it can be approximated by a normal distribution (i.e., are $n p \geq 5$ and $n q \geq 5 ?$ ).a. $n=20, p=0.5$b. $n=10, p=0.6$c. $n=40, p=0.9$

a. Yes b. No c. No

Intro Stats / AP Statistics

Chapter 6

The Normal Distribution

Section 4

The Normal Approximation to the Binomial Distribution

Probability Topics

Piedmont College

Oregon State University

University of St. Thomas

Lectures

0:00

02:53

Check each binomial distri…

08:23

Recall that for use of a n…

08:31

Use the normal approximati…

14:39

04:39

In which of the following …

04:40

a. Use a computer or calcu…

02:29

Find the normal approximat…

02:43

01:32

Probability Distribution A…

04:25

Find the mean, variance, a…

02:48

In order to see what happe…

02:19

Use a computer to find the…

05:32

Use the binomial expansion…

01:15

04:35

02:22

05:09

Consider a binomial experi…

01:43

Find the values $n p$ and …

03:57

Compute the probability of…

04:41

Let $x$ be a binomial rand…

okay for problems. Seven. There's two stipulations that need to be met in order for a binomial distribution to be approximated using a normal distribution. So NP has to be greater than or equal to five, and also en que has to be greater than or equal to five. They both need to be satisfied. So for part, A N P is 20 times 200.5, and that gives us 10. And and Q is going to be 20 times one minus 10.5. Okay, As you know, for Q, she was just one minus p. So one minus 10.5. And that will also give us 10. So both of these are greater than five. Both conditions air satisfied, Part B and P is gonna be 10 times 100.6, and that gives us six. And in Q is gonna be 10 times one minus p, which is one minus 10.6. And that gives us four. Okay, so the first part is greater than five. What? The second part is not okay, So the answer is no again. They both need to be satisfied. Okay. And for part, C N P is gonna be 40 times 400.9 and that gives us 36 and n Q is gonna be 40 times one minus p. And that gives us four. So 36 is greater than five, but four is not. So. This one is no. Okay, so both conditions need to be satisfied.

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