Page 307 - BA2 Integrated Workbook STUDENT 2018

Answers to supplementary objective test questions

CHAPTER 12 – RISK 2: PROBABILITY

12.1 The complete sentences are:

Empirical probabilities can be calculated from samples of past observations.

Subjective probabilities are based on judgement.

Exact probabilities can be applied to the population of outcomes for a certain
event.

12.2 The percentage of containers with contents over 500 ml is 26.43%.

We have a normal distribution with μ = 499.5 and σ = 0.8.

Calculating the z score, we get:
500 – 499.5
z = —————— = 0.625
0.8
Once we have calculated our ‘z score’ we can look this up on the normal
distribution table to find the area under the curve, which equates to the
percentage chance (probability) of that value occurring.

So if we have calculated a z score of 0.625. From the table the value is 0.2357

We want P(x > 500) = P(z > 0.625) = (0.5 – 0.2357) = 0.2643

Therefore, 26.43% of containers will have contents over 500 ml.

12.3 The expected profit is $21,200

Remember the probabilities must sum to 1.0, so the probability of $22,000 must
be 60%.

Profit ($) Probability
50,000 0.2

22,000 0.6
(10,000) 0.2

–––
1.0

–––

EV = ∑px = (50,000 × 0.2) + (22,000 × 0.6) + (–10,000 × 0.2) = $21,200.

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