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Math Help - Continuous Probability

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    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?
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    Quote Originally Posted by EquinoX View Post
    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 .......
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    should z here be 0.3 ? 0.5 - 0.2 = 0.3 then we can find the cutoff value
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    Quote Originally Posted by EquinoX View Post
    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.
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