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Statistics lesson
SaRstats.lgfl.net
Objectives:
To identify normal distributions
To use the standard normal distribution model to evaluate probabilities
Job Requirements
Maths required:
• Probability scales
• Standardising scores
Search and Rescue – sar.lgfl.net
Equipment required:
• Ruler
• Pencil
• Pen
• Calculator
• Normal distribution table
© 2016 London Grid for Learning
Videos
• Introduction to Coastguard rescue teams
• Can you give an example of the Maths involved in your decisions?
Search and Rescue – sar.lgfl.net
© 2016 London Grid for Learning
Standard normal distribution
Normally distributed results can be compared to the standard normal
distribution curve to find probabilities.
0 (sometimes represented
by μ) is the mean of the
data.
σ is a standard deviation.
Search and Rescue – sar.lgfl.net
© 2016 London Grid for Learning
Normal distribution table
Once you find a standardised score (z), you
can find the probability using the table.
e.g. P(0.19) = 0.5753
This means that 0.5753 (57.53%) of the
value are less than 0.19 deviations from
the mean.
Interpret the probabilities as meaning less
than the standardised value.
Search and Rescue – sar.lgfl.net
© 2016 London Grid for Learning
Survivability mean/deviation
Water
Temp (oC)
Mean time
until death
Standard deviation
of time until death
< 0.3°
20 minutes
4 minutes
0.3–4.4°
50 minutes
10 minutes
4.4–10°
120 minutes
22 minutes
10–15.6°
230 minutes
43 minutes
15.6–21.1°
830 minutes
232 minutes
Search and Rescue – sar.lgfl.net
© 2016 London Grid for Learning
Example
We are told that a person has capsized a small boat in waters that are 3.2°. If
we can reach them in 25 minutes, what is the probability that they will die
before we reach them?
1.
Identify how many deviations from the mean this is.
25 - 20 = 5
5 / 4 = 1.25 (divide by the standard deviation
for a standardised score)
2.
Look up this value in the distribution table.
There is an 89.44% chance that they will die.
Search and Rescue – sar.lgfl.net
© 2016 London Grid for Learning