# Thread: what is the difference?

1. ## what is the difference?

Hi all,

In this type normal distribution questions which include "sample", I don't know how to use this sample to solve the question. What is the difference between normal distribution problems and normal sampling questions? I really do have difficulty in solving these type of questions.

2. ## Re: what is the difference?

Surely somewhere in your text book is the fact that if a random variable has mean $\mu$ and standard deviation $\sigma$ then a sample of size n will be (approximately) normally distributed with mean $n\mu$ and standard deviation $\sigma\sqrt{n}$.

3. ## Re: what is the difference?

For the 1st problem:

z= x-μ (x sample)
---------------------
σ/ n (square root)

μ= 95.25
σ= 27.32
n= 25

102.50 - 95.25
-----------------------
27.32 / 25 (square root)

7.25
----- = 1.326 ~ 1.33 = 0.4082
5.464

1-0.4082 = 0.5918

4. ## Re: what is the difference?

For the 2nd problem:

230-237.6
---------------------
26.3 / 55 (square root)

-7.6
= -------------- = -2.143 ~ 2.14
26.3/7.417

= 1-0.9838 = 0.0162

5. ## Re: what is the difference?

I do not know whether or not my answers are correct.

6. ## Re: what is the difference?

Originally Posted by Liliann
For the 1st problem:

z= x-μ (x sample)
---------------------
σ/ n (square root)

μ= 95.25
σ= 27.32
n= 25

102.50 - 95.25
-----------------------
27.32 / 25 (square root)

7.25
----- = 1.326 ~ 1.33 = 0.4082
5.464

1-0.4082 = 0.5918

No.

The probability associated with z-score 1.33 is about 0.907724, not 0.4082 as you have here. Did you forget the 1/2 you sometimes need to adjust your table value?

7. ## Re: what is the difference?

Originally Posted by Liliann
For the 2nd problem:

230-237.6
---------------------
26.3 / 55 (square root)

-7.6
= -------------- = -2.143 ~ 2.14
26.3/7.417

= 1-0.9838 = 0.0162
Nope. You dropped a negative sign.

8. ## Re: what is the difference?

Originally Posted by romsek
Nope. You dropped a negative sign.
Thanks you very much for your help, sir.

I've corrected the mistakes.