What percent of the area under the curve of the standard normal distribution is between -3.232
and z=3.232
(or within 3.232 standard deviations of the mean).
To determine the percentage of the area under the curve of the standard normal distribution between -3.232 and z = 3.232, we need to find the cumulative probability for each value and subtract them.
First, let's find the cumulative probability for -3.232:
P(z < -3.232) = 0.00061
Next, let's find the cumulative probability for z = 3.232:
P(z < 3.232) = 0.99939
To find the area between these two z-scores, we subtract the probability for -3.232 from the probability for 3.232:
P(-3.232 < z < 3.232) = P(z < 3.232) - P(z < -3.232) = 0.99939 - 0.00061 = 0.99878
Therefore, approximately 99.878% of the area under the curve of the standard normal distribution is between -3.232 and z = 3.232.