How to find the area under the standard normal curve between z 1.5 and z 2.5?

It is possible to calculate mathematically the area under the normal curve between any two values of z.

However, tables/software have been developed to give the areas under the normal curve to the left of particular values of z. The function is the probability of Z
The area between two values z1 and z2 (where z2>z1) is therefore

P (Z
For example, to find the area between z1=1.5, z2=2.5

is

P (Z<2.5) - P (Z<1.5)

=0.99379-0.93319

=0.06060

(above values obtained by software, such as R)

For example, the value P (Z<2.5) can be calculated using

P (Z<2.5) = erf (2.5/sqrt (2)) / 2+1/2

where erf (x) is a mathematical function that does not have an explicit formula (calculated by summation of series, or tabulated).