Question

The mean salary of all employees in a company is R3578, with a standard deviation of R1980 Find the probability that for a sample of 38 employees the average salary will be between R3685 and R3783.

Answer 1

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:

`\begin{gathered} Z=\frac{\overline{Z}-\text{ mean}}{\text{ standard deviation/}√(N)} \\ \\ Z=\frac{\overline{Z}-3578}{(1980)/(√(38))} \end{gathered}`

Thus, the probability P that the average salary will be between R3685 and R3783 is given by:

[tex]\begin{gathered} P(3685