[Blindmath] Standard Deviation Question

Sarah Jevnikar sarah.jevnikar at mail.utoronto.ca
Sat Nov 1 21:05:21 UTC 2014

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,

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