Answer :
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<z, or P(Z<z).
The area between two values z1 and z2 (where z2>z1) is therefore
P(Z<z2)-P(Z<z1).
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).
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<z, or P(Z<z).
The area between two values z1 and z2 (where z2>z1) is therefore
P(Z<z2)-P(Z<z1).
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).
We have that for the Question, it can be said that the area under the standard normal curve between z 1.5 and z 2.5 is
P(1.5 &2.5) =0.06
From the question we are told
How to find the area under the standard normal curve between z 1.5 and z 2.5?
Generally the equation for the probability is mathematically given as
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
Where
P(Z < 2.5) = 0.99
P(Z < 1.5) = 0.93
From Z Table
Therefore
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
P(1.5 &2.5) =0.06
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