0% of a normal (of any) distribution falls between z 1.16 and z 1.16. 1.16 - 1.16 = 0.
It is 0.017864
1.16/z = -1.16/z * * * * * No! Pr(Z > 1.16) = 0.123 So Pr(-1.16 < Z < 1.16) = 1 - 2*0.123 = 1 - 0.246 = 0.754
By definition, the 1st 6-tile is the point below which 1/6 of the population falls (irrespective of which distribution is involved). The 2nd 6-tile is the point below which 2/6 of the population falls. This is 100 * 1/3 ~ 33.3% of the population.
95% of the area falls between Z = -1.96 & 1.96.
The area is 0.9270, approx.
It is 0.017864
Pr(Z > 1.16) = 0.123
In a normal distribution half (50%) of the distribution falls below (to the left of) the mean.
Zero.
2
-0.35
Approx 0.995
1.16/z = -1.16/z * * * * * No! Pr(Z > 1.16) = 0.123 So Pr(-1.16 < Z < 1.16) = 1 - 2*0.123 = 1 - 0.246 = 0.754
The standard deviation provides in indication of what proportion of the entire distribution of the sample falls within a certain distance from the mean or average for that sample. If your data falls on a normal (or bell shaped) distribution, a SD of 1 indicates that about 68% of your data points (scores or whatever else) fall within 1 point (plus or minus) of the average (mean) of the data, and 95% fall within 2 points.
The area within the normal curve between -1 standard deviation (SD) and +1 SD is approximately 68%. This means that about 68% of the data falls within one standard deviation of the mean in a normal distribution.
The answer will depend on what the distribution is. Non-statisticians often assum that the variable that they are interested in follows the Standard Normal distribution. This assumption must be justified. If that is the case then the answer is 81.9%
By definition, the 1st 6-tile is the point below which 1/6 of the population falls (irrespective of which distribution is involved). The 2nd 6-tile is the point below which 2/6 of the population falls. This is 100 * 1/3 ~ 33.3% of the population.