Question

I am trying to estimate a binomial experiment, P[X=4] using the normal distribution. Can I do this? Because I know the fact that the P(any single #) for normal is 0. Is there a trick for this? I am trying to estimate a binomial experiment, P[X=4] using the normal distribution. Can I do this? Because I know the fact that the P(any single #) for normal is 0. Is there a trick for this? @Mathematics

Answer 1

the trick is to accomodate for the continuous nature of the normal when approximating the discrete nature of the binomial

Answer 2

the trick itself is to take values that are the average between discretes

Answer 3

Is that the half unit correction?

Answer 4

yes

Answer 5

mean = np

variance = npq

sd = sqrt(var)

Answer 6

Well I've got that, but the question I have would be if this is correct. If I were to take the z probability up to 4, which is a z statistic of -.97. If I were to take the value under that, wouldn't that be the probability of 0, 1, 2, 3 and 4? I want to use it to find the exact value at 4, but I know the integration will be 0 for that...

Answer 7

what are the number of trials: n

and the prob of success: p

???

without those I got no idea

Answer 8

the normal is an approximation; therefore trying to find the exact value at 4 is a bit harsh

Answer 9

n=20, p=.3, q=.7 . The P(X=4)= .130, as I've found from the binomial table

Answer 10

to be exact, youd have to do it with the binomial distribution

Answer 11

That's what I thought! But the question asks for us to do it using the normal distribution. All the questions before it were ranges, but this one is a value, so that's what threw me...

Answer 12

mean = 6 ; sd = sqrt(4.2)

the value under 4 would be:

z = (3.5-6)/sqrt(4.2) = -1.22 as the test statistic

Answer 13

Yeah, I've got that. But I question if the area to the right of this is really the probability of X=4. It seems like it would be the probability of X<=4

Answer 14

i see your point; if its less and equal to 4 then we use the 4.5 if i recall correctly

Answer 15

does the question sate less then 4 or less than equal to 4?

Answer 16

*state

Answer 17

http://people.richland.edu/james/lecture/m170/ch07-bin.html

Answer 18

less than 4 I get .1112

<=4 i get .2327

maybe

Answer 19

No, it is straight =, it is P(x=4), using the normal.

Answer 20

well, equals is just the prob area between 3.5 and 4.5

subtract the normals of 3.5 and 4.5 to approx the bi@4

Answer 21

Ah, thanks!!

Answer 22

yep