# Thread: Continuous Probability

1. ## Continuous Probability

The annual commissions earned bu sales representative of Machine Products, a manufacturer of light machinery, follow the normal distribution. The mean yearly amount earned is $40,000 and the standard deviation is %5,000 The sales manager wants to award the sales representatives who earn the largest commissions a bonus of$1,000. He can award a bonus to 20% of the representatives. What is the cutoff point between those who earns a bonus and those who don't?

2. Originally Posted by EquinoX
The annual commissions earned bu sales representative of Machine Products, a manufacturer of light machinery, follow the normal distribution. The mean yearly amount earned is $40,000 and the standard deviation is %5,000 The sales manager wants to award the sales representatives who earn the largest commissions a bonus of$1,000. He can award a bonus to 20% of the representatives. What is the cutoff point between those who earns a bonus and those who don't?
$\displaystyle z = \frac{x - 40,000}{5,000}$.

Substitute the value of z corresponding to $\displaystyle \Pr(Z > z) = 0.2$ and solve for x .......

3. should z here be 0.3 ? 0.5 - 0.2 = 0.3 then we can find the cutoff value

4. Originally Posted by EquinoX
should z here be 0.3 ? 0.5 - 0.2 = 0.3 then we can find the cutoff value
No, z = 0.8416 (correct to four decinmal places). This is because Pr(Z > 0.8416) = 0.2.