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Exam tomorrow -- help please (z-score table)

  1. Dec 8, 2014 #1
    1. The problem statement, all variables and given/known data
    Let X be a normal random variable with mean 80 and standard deviation 5. What is the probability X is greater than 87? Less than 74?
    I understand how to compute the z score but I'm confused as to when I have to keep the number from the z-table or subtract 1

    2. Relevant equations
    z= x-μ /σ

    3. The attempt at a solution
    z = 1.4
    P (z > 87 ) = ??
    I found the z score to be 0.9192 but do I keep this value as my answer or do I do 1 - 0.9192


    z=-1.2
    P (z < 74)= ??
    again, I found z score to be .1151
    So I keep this value or 1 - 0.1151 and why?
    Thank you
     
  2. jcsd
  3. Dec 8, 2014 #2

    Mark44

    Staff: Mentor

    You need parentheses when you write things like this. It should be z = (x - μ )/σ. As you wrote it, it would be interpreted as z = x - (μ /σ).
    No, the above should be P(X > 87). You get the z-score by transforming the inequality, like so:
    P(X > 87) = ##P(\frac{X - 80}{5} > \frac{87 - 80}{5}) = P(z > \frac{7}{5}) = P(z > 1.4)##

    No, the z-score is 1.4, and the probability associated with it is 0.9192. This probability is the area under the standard normal curve (the "bell curve") between -∞ and 1.4.

    It's very helpful to draw a quick sketch of the bell curve, including your z-score and the probability value you get from the table. With a sketch you can easily see which area under the curve you're interested in.
     
    Last edited: Dec 9, 2014
  4. Dec 9, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    As Mark44 has said: draw a picture---even a very crude (but symmetric) picture will do. For any z, P(Z<z) is the area to the left of the point z under the graph of the unit normal density, so if z < 0, P(Z < z) < P(Z < 0) = 1/2, while P(Z > z) > P(Z > 0) = 1/2. So, if you are given a probability value P(Z < z ) < 1/2 or P(Z > z) > 1/2, you know that z < 0. If you are given the opposites of these, you know that z > 0.
     
  5. Dec 10, 2014 #4
    Thank you both
    Did well on my exam
     
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