Episode 16: Actuarial science and normal distributions

This week the topic was statistical distributions and actuarial science. We interviewed Richard Harland, who works in risk management for an insurance firm. We talked to him about his work as an actuary, and how he uses statistical distributions like the normal distribution to predict the probability of risky events.

Interesting links:

• Normal distribution on Wikipedia
• Normal distributions at Maths Is Fun
• Introduction to being an actuary at the Actuarial Institute website
• Be an actuary website

Puzzle: Your factory packages crisps into bags using a machine which isn’t completely accurate and the weight of crisps which ends up in each bag varies according to a normal distribution.

The mean weight of a bag is 154g, and the standard deviation is 8g. The bags are labelled as containing 150g of crisps, but 31% of bags produced by the machine are underweight. To what value should you change your mean weight to make sure 95% of bags weigh more than 150g?

Solution:

On a normal distribution curve, 95% of values will fall within two standard deviations of the mean. This means in order to ensure 95% of crisp packets weigh 150g or more, we need 150g to be two standard deviations away from the mean - so the mean needs to be 150g + (2 x 8g) = 166g.