Answer to Question #242232 in Statistics and Probability for Vee

Question

1.3 The monthly salaries of the employees at Lyman Limited follow a normal distribution with an average salary of R 14 000 and a standard deviation of R 500.

a) What percentage of employees get paid between R 13 000 and R 15 500?

Answer 1

$\mu = 14000 \\ \sigma=500 \\ P(13000<X<15500) = P(X<15500) -P(X<13000) \\ =P(Z< \frac{15500-14000}{500}) -P(Z< \frac{13000-14000}{500}) \\ = P(Z< 3) -P(Z< -2) \\ = 0.9986 -0.0227 \\ = 0.9759 \\ = 97.59 \; \%$