Respuesta :
Solution:
Given;
A data set of values has a mean of 45 and standard deviation of 5.
The z-score for a point A is 0. The z-score for a point B is 0.2.
To find the values of A and B, we will apply the z-score formula, which is
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ Where\text{ } \\ x\text{ is the observed value} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]Where
[tex]\begin{gathered} \mu=45 \\ \sigma=5 \end{gathered}[/tex]For the value of point A,
Where, z = 0 for point A
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 0=\frac{x-45}{5} \\ Crossmultiply \\ 5(0)=x-45 \\ 0=x-45 \\ x=45 \end{gathered}[/tex]Hence, the value of point A is 45
For the value of point B,
Where, z = 0.2 for point B
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 0.2=\frac{x-45}{5} \\ Crossmultiply \\ 0.2(5)=x-45 \\ 1=x-45 \\ Collect\text{ like terms} \\ x=1+45=46 \\ x=46 \end{gathered}[/tex]Hence, the value of point B is 46
