# Probability of a return from historical average and standard deviation

I have a question from a sample exam paper that I'm having some trouble figuring out.

The question is: Bavarian Sausage stock has an average historical return of 16.3% and a standard deviation of 5.3%. What is the probability that the return on Bavarian Sausage will be less than 11%?

ANS: 16% 1-.5-.34 = .16

The answer provided shows the upper and lower values to be .5 and .34 (50% and 34%). How do you arrive at these figures?

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The answer assumes a normal distribution.

As you can see in this graph, in the normal distribution:

• 50% of the outcomes are in the right hand part of the distribution (i.e. higher than the mean)
• 34% of the outcomes are between the mean and 1 standard deviation

The question wants you to determine the probability that your stock returns less than 11%. If you notice that the 11% are exactly 1 standard deviation away from the mean (11% = 16.3%-5.3%) you know that you can compute the probability by doing:

1 (all the outcomes) - 0.5 (all the outcomes above the mean) - 0.34 (outcomes between mean and standard deviation, below the mean).

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