CIMA P1 Syllabus D. Dealing With Risk And Uncertainty - Normal Distribution - Notes ^{5 / 5}

- is probability (%) of something happening (eg. achieving a profit) based on standard deviation and average (mean).

This formula is given in the exam:

Z = (x - µ) / Ϭ

• where:
  Z is a Z-score = probability % - from the mean to variable X  (use Normal distribution table);
  μ is the mean (average) = the Most popular figure 
  σ is the standard deviation = how far away from the average you are

Normal Distribution Table

This is given in the exam

Illustration 1

Average profit is $100
Std deviation $10

What is the probability of profit being more than $105?

Step by step

1. Step 1. Calculate Z-score

   Z = (x - µ) / Ϭ
   Z = (105 - 100) / 10
   Z = 5 / 10 = 0.5

2. Step 2. Find the % in the Table

   Find Z value of 0.5 in the first column = 0.1915 or 19.15%

3. Step 3. Calculate the probability of profit being more than $105.

   Less than $105 = 50% + 19.15% = 69.15%
   Greater than $105 = 50% - 19.15% = 30.85%

Illustration 2

Average (Expected value) profit from a project is $200,000
Standard deviation is  $100,000. 

If the project loses more than $50,000 the company will be in financial difficulties.

What is the probability of the project losing more than $50,000?

1. Step 1. Calculate Z-score

   Z = (x - µ) / Ϭ
   Z = (-50,000 - 200,000) / 100,000 
   Z = 2.5

2. Step 2. Find the % in the Table

   Find Z value of 2.5 in the first column = 0.4938 or 49.38%

3. Step 3. Calculate the probability of the project losing MORE than $50,000 is:

   Less than $50,000 = 50% + 49.38% = 99.38%
   Greater than $50,000  = 50% - 49.38% = 0.62%

So we have a 99.38% confidence that losses won't fall lower than 50k

Another way of saying this is the value at risk is 50,000 when we have a 99.38% confidence level