1. To identify normal distributions
Statistics lesson
SaRstats.lgfl.net
Objectives:
To identify normal distributions
To use the standard normal distribution model to evaluate probabilities

2. Job Requirements Maths required: Equipment required:
Probability scales
Ruler
Standardising scores
Pencil
Pen
Calculator
Normal distribution table

3. Videos Introduction to Coastguard rescue teams
Can you give an example of the Maths involved in your decisions?

4. 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.

5. Normal distribution table
Once you find a standardised score (z), you can find the probability using the table. e.g. P(0.19) = This means that (57.53%) of the value are less than 0.19 deviations from the mean. Interpret the probabilities as meaning less than the standardised value.

6. 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

7. 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?
Identify how many deviations from the mean this is.
= 5
5 / 4 = 1.25 (divide by the standard deviation
for a standardised score)
Look up this value in the distribution table.
There is an 89.44% chance that they will die.