We need to find the probability the average salary will be between R3685 and R3783 for a sample of 38 employees.
We know that the mean salary of the population is R3578 and its standard deviation is R1980.
Thus, the z-score Z of the sample of N = 38 employees is given by:
[tex]\begin{gathered} Z=\frac{\overline{Z}-\text{ mean}}{\text{ standard deviation/}\sqrt{N}} \\ \\ Z=\frac{\overline{Z}-3578}{\frac{1980}{\sqrt{38}}} \end{gathered}[/tex]Thus, the probability P that the average salary will be between R3685 and R3783 is given by:
[tex]\begin{gathered} P(3685