Question

The income pay to workers in senior carder in a company where group into three and summary as follows;15%of the workers where in a group A 30%of d workers where in group B and 55% of the workers are in group C.if u receive an alert less than #25,000 you are in group C,if u receive more than #56,000 you are in group A. find the mean and the standard deviation of the income distribution assume it is normal distributed.

Answer 1

Let $X=$ income: $X\sim N(\mu, \sigma^2)$

$$P(X>56000)=1-P(X<56000)$$

$$=1-P(Z<\dfrac{56000-\mu}{\sigma})=0.15$$

$$\dfrac{56000-\mu}{\sigma}\approx1.036433$$

$$P(X<25000)=P(Z<\dfrac{25000-\mu}{\sigma})=0.55$$

$$\dfrac{25000-\mu}{\sigma}\approx0.125661$$

$$56000-1.036433\sigma=25000-0.125661\sigma$$

$$\sigma\approx34037$$

$$\mu=35000-0.125661(34037)\approx20723$$

$\mu=20723, \sigma=34037$