Question

Find the area under the standard normal probability distribution between the following pairs of z-scores:

a)$\mathbf{z}\mathbf{=}\mathbf{0}\mathbf{}\mathbf{and}\mathbf{}\mathbf{z}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{00}$

b)$\mathbf{z}\mathbf{=}\mathbf{0}\mathbf{}\mathbf{}\mathbf{and}\mathbf{}\mathbf{z}\mathbf{=}\mathbf{3}$

c)$\mathbf{z}\mathbf{=}\mathbf{0}\mathbf{}\mathbf{and}\mathbf{}\mathbf{z}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5}$

d)$\mathbf{z}\mathbf{=}\mathbf{0}\mathbf{}\mathbf{and}\mathbf{}\mathbf{z}\mathbf{=}\mathbf{.}\mathbf{80}$

Short answer

A probability distribution is a statistical distribution that specifies all potential values as well as potential outcomes for a random variable within a particular range. The likelihood of an event happening. A probability distribution is a table as well as a formula that associates every result of a statistical study with its occurrence probability.

Step-by-step solution

(a) The data is given below

The calculation is given below:

$\text{z}=0\text{andz}=2$

To find the area between 0 and 2 are:

$\text{P}(0<\text{z}<2)=0.4772$

The chart is given below:

(b) The data is given below

The calculation is given below:

$\text{z}=0\text{andz}=3$

To find the area between 0 and 3 are:

$\text{P}(0<\text{z}<3)=0.4987$

The chart is given below:

(c) The data is given below

The calculation is given below:

$\text{z}=0\text{andz}=1.5$

To find the area between 0 and 1.5 are:

$\text{P}(0<\text{z}<1.5)=0.4332$

The chart is given below:

(d) The data is given below

The calculation is given below:

$\text{z}=0\text{andz}=0.80$

To find the area between 0 and 0.80 are:

$\text{P}(0<\text{z}<0.80)=0.2881$

The chart is given below: