[Blindmath] Standard Deviation Question

[Sarah Jevnikar]

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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