Calculating percentile given z score












0












$begingroup$


What is the formula to convert a z-score to its appropriate percentile?
I have not found an answer on this site nor on Google. I assume there is a formula.






probability statistics







share|cite|improve this question









$endgroup$












  • $begingroup$
    You mean... the area?
    $endgroup$
    – Sean Roberson
    Dec 7 '18 at 4:27










  • $begingroup$
    If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
    $endgroup$
    – BGM
    Dec 7 '18 at 6:59
















0












$begingroup$


What is the formula to convert a z-score to its appropriate percentile?
I have not found an answer on this site nor on Google. I assume there is a formula.






probability statistics







share|cite|improve this question









$endgroup$












  • $begingroup$
    You mean... the area?
    $endgroup$
    – Sean Roberson
    Dec 7 '18 at 4:27










  • $begingroup$
    If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
    $endgroup$
    – BGM
    Dec 7 '18 at 6:59














0












0








0





$begingroup$


What is the formula to convert a z-score to its appropriate percentile?
I have not found an answer on this site nor on Google. I assume there is a formula.






probability statistics







share|cite|improve this question









$endgroup$




What is the formula to convert a z-score to its appropriate percentile?
I have not found an answer on this site nor on Google. I assume there is a formula.






probability statistics




probability statistics






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 7 '18 at 2:07









JinzuJinzu

381413




381413












  • $begingroup$
    You mean... the area?
    $endgroup$
    – Sean Roberson
    Dec 7 '18 at 4:27










  • $begingroup$
    If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
    $endgroup$
    – BGM
    Dec 7 '18 at 6:59


















  • $begingroup$
    You mean... the area?
    $endgroup$
    – Sean Roberson
    Dec 7 '18 at 4:27










  • $begingroup$
    If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
    $endgroup$
    – BGM
    Dec 7 '18 at 6:59
















$begingroup$
You mean... the area?
$endgroup$
– Sean Roberson
Dec 7 '18 at 4:27




$begingroup$
You mean... the area?
$endgroup$
– Sean Roberson
Dec 7 '18 at 4:27












$begingroup$
If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
$endgroup$
– BGM
Dec 7 '18 at 6:59




$begingroup$
If $X sim mathcal{N}(mu, sigma^2)$, then for a certain quantile $q$ and the corresponding z-score $z$ will satisfy $q = mu + sigma z$. If you are interested in the CDF $Pr{X leq q}$ instead, you will need a numerical method to compute that integral - either pre-computed table or statistical software.
$endgroup$
– BGM
Dec 7 '18 at 6:59










1 Answer
1






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0












$begingroup$

If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
$$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$



Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.



For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.






share|cite|improve this answer









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    1 Answer
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    1 Answer
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    $begingroup$

    If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
    $$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$



    Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.



    For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
      $$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$



      Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.



      For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
        $$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$



        Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.



        For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.






        share|cite|improve this answer









        $endgroup$



        If $z$ is the $z$-score, then you get the corresponding percentile $p_z$ by
        $$ p_z =left lceil {P(Z leq z)cdot 100 } right rceil$$



        Here $left lceil x right rceil$ is the ceiling function $left lceil x right rceil = min {p in mathbb{Z}| p geq x }$ and $Z sim N(0,1)$.



        For example, you may find $P(Z leq z)$ here for $z = 1.2$ using WolframAlpha and obtain that this score belongs to the $89^{mbox{th}}$ percentile.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 7 '18 at 8:07









        trancelocationtrancelocation

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        10.5k1722






























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