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Math Help - I'm stuck with this hard probability question

  1. #1
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    Question Normal Random Variables - Can anyone guide me to do the rest of the problem

    A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 89 meters and a standard deviation 190 meters.
    What is the probability that the measured distance will be smaller than the true distance?


    I interpreted the question as this: what is the probability that the "overestimate" is less than zero? (Do you think I interpreted it right?)

    Then, I expressed the difference between the mean (89) and 0 as a number of standard deviations:
    89/190= 0,4684

    but now I'm stuck... Can anyone help me to do the rest of the question?

    Appreciate any responds.
    Last edited by essedra; December 11th 2009 at 11:37 AM. Reason: To be more descriptive for the title
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  2. #2
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    Quote Originally Posted by essedra View Post
    A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 89 meters and a standard deviation 190 meters.
    What is the probability that the measured distance will be smaller than the true distance?

    I interpreted the question as this: what is the probability that the "overestimate" is less than zero? (Do you think I interpreted it right?)

    Then, I expressed the difference between the mean (89) and 0 as a number of standard deviations:
    89/190= 0,4684

    but now I'm stuck... Can anyone help me to do the rest of the question?

    Appreciate any responds.
    Calculate Pr(X < 0) where X ~ Normal(mean = 89, sd = 190).
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