3. You decide to embark on a small business enterprise and estimate that the profit in the first year, X, will vary between R0 and R10000 with the probabilities in Table 5.12 (Negative profits represent a loss.) Table 5.12: Data set X 0 2500 5000 7500 10000 P(X) 0.053 0.317 0.581 0.037 0.012 Calculate a) The expected profit (rounded off to zero decimals). b) The variance (rounded off to zero decimals). c) The standard deviations (rounded off to four decimals
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
3. You decide to embark on a small business enterprise and estimate that the profit in the first year, X, will
vary between R0 and R10000 with the probabilities in Table 5.12 (Negative profits represent a loss.)
Table 5.12: Data set
| X | 0 | 2500 | 5000 | 7500 | 10000 |
| P(X) | 0.053 | 0.317 | 0.581 | 0.037 | 0.012 |
Calculate
a) The expected profit (rounded off to zero decimals).
b) The variance (rounded off to zero decimals).
c) The standard deviations (rounded off to four decimals)
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