[Blindmath] Standard Deviation Question

Sun Nov 2 00:26:21 UTC 2014

Hi,
Hmmm, I think I know what went wrong: a lot of times, statistics requires
that you look closely at what is being asked. Statistics, like any other
mathematics disciplines, requires careful attention to detail and wording.
In this case, the question asked about "faster time", which in this case
means earlier times. Do not worry about Z-scores now and your brain being
"fried" - it might be wrong impression you've got somehow that "faster time"
meant later times.
Cheers,
Joseph

-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Sarah
Jevnikar via Blindmath
Sent: Saturday, November 1, 2014 5:15 PM
To: 'Blind Math list for those interested in mathematics'
Subject: Re: [Blindmath] Standard Deviation Question

Thank you Marana and Joseph! I did some looking up after writing initially,
and figured out the following.
Standardization has to happen. Except that I found the Z-Score for a
probability of 0.95, which is all but the rightmost tail of the
distribution. This gives a Z-score of 1.645 and a swim time of 5.187,
neither of which make sense. I can't think of the intuition as to why I'd be
looking at the left 5% tail though; my brain must be fried. Any thoughts on
this? Google's not making it clear and I don't have my stats books handy.

-----Original Message-----
From: Ramana Polavarapu [mailto:sriramana at gmail.com]
Sent: November-01-14 5:56 PM
To: Joseph Lee; Blind Math list for those interested in mathematics
Cc: Sarah Jevnikar
Subject: Re: [Blindmath] Standard Deviation Question

Obviously, there are better statisticians than I am on this group.
Joseph has answered your question.  The main thing is to figure out the area
under the curve equal to 90%.  Here is my thinking:
1. She is better than 90%.
2. If she hits the mean (4.2), she is better than 50%.
3. We need to get rid of 40% below (left of) mean.
4. By looking at the tables, you can figure out 1.28 standard deviations
equal to 40%.
5. The answer should be 4.2 - 1.28 times .6.
I have looked at the following web site to get this answer:
http://www.dummies.com/how-to/content/how-to-find-a-percentile-for-a-normal-
distribution.html
Look at the fish example mentioned there.

Thank you.

Regards,

Ramana

On 11/2/14, Joseph Lee via Blindmath <blindmath at nfbnet.org> wrote:
> Hi,
> I think you meant 4.2, not 4.52. If it was 4.52, then two standard 
> deviations must be 3.32-5.72. Also, faster than 95% implies that 
> Sally's time should be shorter (3.0-3.32). In reality, Sally's time is:
> 4.52 (or 4.2) - (sigma of 1.95 * 0.6).
> As a normal distribution is shaped like a bell (really a cone with a 
> smooth U at the top) with an imaginary line running down the center of 
> it, a standard deviation measures how data is spread out on the center 
> of the bell. Thus, one standard deviation will denote data range 
> between top 16% to bottom 16%, two standard deviation measures from 
> top 2.5% to bottom 2.5% and so on (what I mean by "top" and "bottom"
> are really left and right sides; so half of a data that lies within 
> one standard deviation will be on the immediate left of the center 
> line). The concept of normal distribution and the bell curve shows up 
> again when a student studies about inference and standard error.
> Cheers,
> Joseph
>
> -----Original Message-----
> From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of 
> Sarah Jevnikar via Blindmath
> Sent: Saturday, November 1, 2014 2:05 PM
> To: 'Blind Math list for those interested in mathematics'
> Subject: [Blindmath] Standard Deviation Question
>
> Hi all,
> I'm helping a friend out with stats homework, but I can't remember the 
> specifics of a normal distribution and don't have a tactile diagram handy.
> I'm wondering if someone could help me fill in the gaps.
>
> The question reads:
> "The average swim time for a 200m race was 4.52min with a standard 
> deviation of .60min. Sally swam faster than 95% of her competitors in 
> the race. What was Sally's race time?"
>
> My thinking was as follows:
> The standard deviation of 0.6 min and the six sigma rule that states 
> 68% of data is in the first sd, 95 in the second, and 99 in the 3rd,
should apply.
> This would mean that 68% of swimmers would have times between 3.6 and 4.8.
> Then 95% of swimmers should have times between 3.0 and 5.4. If sally 
> is faster than 95% of swimmers, would this make her time 5.4? I'm 
> thinking not but I'm not sure what I'm missing.
> Thank you as always for your help,
> Sarah
>
>
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