Suppose that for a given computer salesperson, the table below gave the probability distribution of x = the number of systems sold in 1 month. X 1 2 3 4 5 6 7 8 P(x) 0.01 0.12 0.10 0.30 0.30 0.11 0.01 0.05 Calculate the mean value of x (the mean number of systems sold). Calculate the variance and standard deviation of x. How would you interpret the variance and standard deviation of x?
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!
Suppose that for a given computer salesperson, the table below gave the
|
X |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
P(x) |
0.01 |
0.12 |
0.10 |
0.30 |
0.30 |
0.11 |
0.01 |
0.05 |
- Calculate the
mean value of x (the mean number of systems sold). - Calculate the variance and standard deviation of x.
- How would you interpret the variance and standard deviation of x?
Given
The probability distribution of systems sold in 1 month
Where X represents the number of systems
Calculate:
- Mean
- variance, standard deviation
- give the Interpretation using variance and standard deviation
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