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Hi,
Find the z-scores for which 90% of the distribution's area lies between -z and z.
-1.6449 < z < 1.6449 Excel function: NORMSINV(.05) = 1.64485
For the normal distribution:
one standard deviation from the mean accounts for about 68.2% of the set
two standard deviations from the mean account for about 95.4%
and three standard deviations from the mean account for about 99.7%.
Important to Understand z -values as they relate to the Standard Normal curve:
Below: z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.
Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50% to the right
a a/2 2-tailed crtical regions
80% 0.2 10% z <-1.28155 z >+1.28155
90% 0.1 5% z <-1.645 z >+1.645
92% 0.08 4% z <-1.751 z >+1.751
95% 0.05 2.50% z <-1.96 z >+1.96
98% 0.02 1% z <-2.326 z >+2.326
99% 0.01 0.50% z<-2.576 z >+2.576
