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S2Student

Guest

I'm Stuck on A Sampling Question

I'm stuck on this question which asks:

The random variable X has a B(40,0.3) distribution. The mean of a random sampre of n observations of X is denoted by

. Find

a) P(

≥13)
b) the smallest value of n for which P(

≥13) < 0.001

I'm currently more stuck on the first one, I think I might be able to get the second part done if I know how to do the first one. So, we've been taught that we can approximate the Binomial by a Normal.

And so I get X~N(12,8.4)

We have also been taught that when you are taking many sample means, then

~N(12,8.4/40)

So does that mean that

P(

≥13 = P(Z≥(13-(1/80)-12)/(√(8.4/40))

= P(Z≥2.155)
= 1-Φ(2.155)
=1-0.9846
= 0.0154

?

That's the answer that I keep on getting, but the book has a different answer. By the way, my book tells me the continuity correction for these kind of samplings is 1/2n, hence the 1/80. What am I doing wrong? The answer in the book says 0.0084.

Thank you for your help!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: I'm Stuck on A Sampling Question

Hi S2Student;

B(40,.3) can be approximated by N(12,2.89827).

This approximation may be improved by using a continuity correction. Remember the Binomial distribution is discrete and the Normal is continuous.

Now just convert 2.89827 to a z-score to find a)

Also please check here for all you want about Binomial and Normal distributions.

http://en.wikipedia.org/wiki/Binomial_distribution

Last edited by bobbym (2009-11-14 16:48:14)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Sakrit

Member

Registered: 2016-06-29

Posts: 1

Re: I'm Stuck on A Sampling Question

The thing is your book tells 49 not 40

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: I'm Stuck on A Sampling Question

Hmmm, a cyptic comment if ever there was one. What is 49? What book?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.