Standard Normal Distribution
This is an illustration of the Standard Normal Distribution.
STANDARD NORMAL DISTRIBUTION:
Standard normal distribution is a continuous, symmetric, bell-shaped distribution
of a variable.
The known characteristics of the normal curve make it possible to estimate the
probability of occurrence of any value of a normally distributed variable.
Properties:
1. The distribution is bell-shaped.
2. The mean, median, and mode are equal and are located at the center of the
distribution.
3. The mean is located at z=0.
4. The distribution is unimodal.
5. The distribution is continuous.
6. The distribution is asymptotic. ( it never touches the x-axis )
7. The distribution is symmetric about the mean.
8. The total area under the curve is 1.00 or 100%.
, 9. The area under the part of the normal curve that lies within 1 standard deviation of
the mean is about 68.27%, within 2 standard deviations is about 95.45%, within 3
standard deviations is about 99.73%.
A normal distribution can be converted to a standard normal distribution by
obtaining the z value( z- scores ).
The normal distribution property allows computing a probability problem concerning x
into one concerning z.
To determine the probability that x lies in a given interval, converting the interval into z
scale and then compute the probability by using the standard normal distribution table.
This is an illustration of the Standard Normal Distribution.
STANDARD NORMAL DISTRIBUTION:
Standard normal distribution is a continuous, symmetric, bell-shaped distribution
of a variable.
The known characteristics of the normal curve make it possible to estimate the
probability of occurrence of any value of a normally distributed variable.
Properties:
1. The distribution is bell-shaped.
2. The mean, median, and mode are equal and are located at the center of the
distribution.
3. The mean is located at z=0.
4. The distribution is unimodal.
5. The distribution is continuous.
6. The distribution is asymptotic. ( it never touches the x-axis )
7. The distribution is symmetric about the mean.
8. The total area under the curve is 1.00 or 100%.
, 9. The area under the part of the normal curve that lies within 1 standard deviation of
the mean is about 68.27%, within 2 standard deviations is about 95.45%, within 3
standard deviations is about 99.73%.
A normal distribution can be converted to a standard normal distribution by
obtaining the z value( z- scores ).
The normal distribution property allows computing a probability problem concerning x
into one concerning z.
To determine the probability that x lies in a given interval, converting the interval into z
scale and then compute the probability by using the standard normal distribution table.
