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Math Help - A few basic Standard Normal Probability Distribution problems

  1. #1
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    A few basic Standard Normal Probability Distribution problems

    Hello, I got a few problems I need help with, they shouldnt be much work, and I have the answers I just dont know how to get them.

    I dont know how common it is for an elementary statistics book to come with a chart that has z scores, and area on it, but thats what im supposed to be using. Ill try to give you as much info as possible to make this as easy as it can be for you

    Standard Normal Distribution: Assuming the readings on the thermometers are normally distributed with a mean of 0 degrees and a standard deviation of 1.00 degrees Celsius. a thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of the reading (The given values are in celsius degrees)

    Some of these are very easy, for example "less than -1.00", where I can just look up the z score of -1.0 and get the area, which is .1587 which is the answer im looking for

    However ones like, Greater than 3.52 confuse me, for the simple fact that I have to look at -3.52 to get the correct area. Can anyone explain why?

    Also, and more importantly, the question P(z<-2.575 or z>2.575) (mean:0 std:1) confuses me, the answer is .0100, but I cant get it to work. Tbh im not even sure what to do with this one, im sure its simple. the area for 2.575 =.9950 and the area for -2.575 = .0050
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  2. #2
    MHF Contributor matheagle's Avatar
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    FIRST of all, two numbers that are not equal to each other are not equal
    You do not mean 2.575 =.9950, which is the problem.
    Every stat book has a N(0,1) table and this Z random variable is symmetric about Zero
    so

    P(Z<-3.52)=P(Z>3.52)

    your book most likely has the cummulative distribution of Z, which is summing (integrating)
    up the probabilities.

    F_Z(z)=P(Z<z)=\int_{-\infty}^z{e^{-u^2/2}\over \sqrt{2\pi}}du

    You mean P(Z<2.575 )=.995
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