# Continuous Probability

• May 27th 2008, 02:07 PM
EquinoX
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?
• May 27th 2008, 04:46 PM
mr fantastic
Quote:

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?

$z = \frac{x - 40,000}{5,000}$.

Substitute the value of z corresponding to $\Pr(Z > z) = 0.2$ and solve for x .......
• May 27th 2008, 05:15 PM
EquinoX
should z here be 0.3 ? 0.5 - 0.2 = 0.3 then we can find the cutoff value
• May 27th 2008, 06:57 PM
mr fantastic
Quote:

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.