# Thread: sample percentage contained within symmetric limits

1. ## sample percentage contained within symmetric limits

Hi!
Thank you in advance for assisting with my question.
I am working on a probability question and am able to answer almost all of it except one final part. The answer reads: " The probability is 95% that the sample percentage will be contained within 6.94% symmetrically around the population mean." I can not figure out how the 6.94% was obtained. I realize that .0694 equals the Z value -1.48, but that doesn't help me.

The full question is "The probability is 95% that the sample percentage will be contained within what symmetrical limits of the population percentage."
Here is my work:
n = 200,
π = .5
p = .5

1-.95 =.5
.5/2= .0250
Z value of .0250 = -1.96
Z value of .9750 (.95 + .0250 =.9750) is +1.96

-1.96 <Z <+1.96

A = .5 + (1.96 * .0354) =.5694
B = .5 – (1.96* .0354) =.4306

I searched in my textbook, other statistic books and online, but still can not figure this out.
Any help would be greatly appreciated.
Thanks,

2. ## Re: sample percentage contained within symmetric limits

Originally Posted by ealeql
Hi!
Thank you in advance for assisting with my question.
I am working on a probability question and am able to answer almost all of it except one final part. The answer reads: " The probability is 95% that the sample percentage will be contained within 6.94% symmetrically around the population mean." I can not figure out how the 6.94% was obtained. I realize that .0694 equals the Z value -1.48, but that doesn't help me.

The full question is "The probability is 95% that the sample percentage will be contained within what symmetrical limits of the population percentage."
Here is my work:
n = 200,
π = .5
p = .5

1-.95 =.5
.5/2= .0250
Z value of .0250 = -1.96
Z value of .9750 (.95 + .0250 =.9750) is +1.96

-1.96 <Z <+1.96

A = .5 + (1.96 * .0354) =.5694
B = .5 – (1.96* .0354) =.4306

I searched in my textbook, other statistic books and online, but still can not figure this out.
Any help would be greatly appreciated.
Thanks,
I suspect that what your textbook is getting at is that using the difference between the upper and lower limits of your interval we can obtain:

(.5694 - .4306) / 2 = ( .1388) /2 = .0694 or 6.94%.

Is that correct--- or am I right?

3. ## Re: sample percentage contained within symmetric limits

Originally Posted by Dragan
Is that correct--- or am I right?

4. ## Re: sample percentage contained within symmetric limits

Thank you very much of answering this question. I really appreciate it.

 Tweet

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts