Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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Step 1
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.
Step 2
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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