n a summary report given by Ing. Pobbi on the lengths of iron rods produced by two machines, he stated that the variability of machine A was higher compared to that of machine B. Critique the report of the Engineer given data on the length of rods produced given as; MachineA(cm): 380 410 280 310 305 360 270 355 400 Machine B(m): 1.1 1.3 1.2 2.0 1.5 1.6 1.4 1.6 1.7
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!
In a summary report given by Ing. Pobbi on the lengths of iron
rods produced by two machines, he stated that the variability of
machine A was higher compared to that of machine B. Critique
the report of the Engineer given data on the length of rods
produced given as;
| MachineA(cm): | 380 | 410 | 280 | 310 | 305 | 360 | 270 | 355 | 400 |
| Machine B(m): | 1.1 | 1.3 | 1.2 | 2.0 | 1.5 | 1.6 | 1.4 | 1.6 | 1.7 |
Calculating variance for both machine
| Machine A (cm) | Machine A (m) | (X-Mean)^2 | Machine B (m) | (X-Mean)^2 |
| 380 | 3.8 | 0.151 | 1.1 | 0.151 |
| 410 | 4.1 | 0.475 | 1.3 | 0.036 |
| 280 | 2.8 | 0.373 | 1.2 | 0.083 |
| 310 | 3.1 | 0.097 | 2 | 0.261 |
| 305 | 3.05 | 0.130 | 1.5 | 0.000 |
| 360 | 3.6 | 0.036 | 1.6 | 0.012 |
| 270 | 2.7 | 0.506 | 1.4 | 0.008 |
| 355 | 3.55 | 0.019 | 1.6 | 0.012 |
| 400 | 4 | 0.347 | 1.7 | 0.045 |
| Total=30.7 | Total=2.134 | Total=13.4 | Total=0.608 |
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