Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 human errors and 3 machine errors on the same day? State your answer as a decimal value rounded to two digits after the decimal point.
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!
Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following
|
Number of human errors |
||||||
|
No. of Tech Errors |
|
0 |
1 |
2 |
3 |
Total |
|
0 |
8 |
6 |
4 |
4 |
22 |
|
|
1 |
5 |
8 |
9 |
10 |
32 |
|
|
2 |
4 |
5 |
10 |
8 |
27 |
|
|
3 |
0 |
3 |
4 |
12 |
19 |
|
|
Total |
17 |
22 |
27 |
34 |
100 |
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