To calculate normal distributions values must be?
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!
| To calculate |
Standard normal distribution:
The standard normal distribution is a special case of normal distribution, in which the mean of the distribution is 0 and standard deviation of the distribution is 1. The Z-scores for the given sample size can be calculated using the given formula.
The procedure for obtaining the percentage of all the possible observations that lie within the specified range is as follows:
- Sketch the normal curve associated with the variable.
- Shade the region of interest and mark the delimiting x-values.
- Compute the z-scores for the x-
- Find the area under the standard normal curve for the computed z-scores using standard normal table.
Several tests of normality exist, using which you can verify whether a particular data follows the normal distribution.
Usually, before conducting a formal test, we prefer to take the help of graphical methods, to see if the data may be assumed to follow the normal distribution, at least approximately. A few such graphical methods are:
- Histogram of the data , superimposed with a normal probability curve,
- Normal probability plot with confidence interval,
- Normal quantile-quantile (QQ) plot.
- Boxplot, etc.
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