Hi

this is my first time in this web site, and it'd be really great if I could get some help from some nice ppl in here!

So I was doing this problem in the text book,

and I got confused about the normal approximation. (I think it should be pretty basic, but it's something I just don't get)

Problem1:

p1.jpg

Soln1:

s1.jpg

This is pretty straight forward, and I do understand the whole process

But then,

Problem2:

p2.jpg

Soln2:

s2.jpg

You can notice that, for the Problem2, 0.5 was substracted from 15,

in order to minimize the error occurring when measuring binomial distribution with normal distribution (or whatever else for the reason)

However, that does not applied to Problem1, 55 stays 55!

If we substract .5, we'll get an answer of .24 which is not the right answer.

But then, if we don't substract .5 from Problem2, we get the answer of 0.06, which is not an option.

But I just want to know when we take the 0.5 off.

I remember some info from internet that, as long as n is quite large and p is close to 0.5, we use the normal approximation for the binomial.

But how close is close enough, and how large is large enough?

It said as long as np>5, it is considered as enough large and close

But for the Problem1, np is 60, which is quite larger than 5 :skeptical:

Can anybody give me some insight?

I'd greatly appreciate that.

this is my first time in this web site, and it'd be really great if I could get some help from some nice ppl in here!

So I was doing this problem in the text book,

and I got confused about the normal approximation. (I think it should be pretty basic, but it's something I just don't get)

Problem1:

p1.jpg

Soln1:

s1.jpg

This is pretty straight forward, and I do understand the whole process

But then,

Problem2:

p2.jpg

Soln2:

s2.jpg

You can notice that, for the Problem2, 0.5 was substracted from 15,

in order to minimize the error occurring when measuring binomial distribution with normal distribution (or whatever else for the reason)

However, that does not applied to Problem1, 55 stays 55!

If we substract .5, we'll get an answer of .24 which is not the right answer.

But then, if we don't substract .5 from Problem2, we get the answer of 0.06, which is not an option.

But I just want to know when we take the 0.5 off.

I remember some info from internet that, as long as n is quite large and p is close to 0.5, we use the normal approximation for the binomial.

But how close is close enough, and how large is large enough?

It said as long as np>5, it is considered as enough large and close

But for the Problem1, np is 60, which is quite larger than 5 :skeptical:

Can anybody give me some insight?

I'd greatly appreciate that.

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