[Blindmath] Standard Deviation Question

[Joseph Lee]

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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