Reversing the PDF Formula

[gtsikhanovich]

Hello, I am writing a Math IA for my IB Diploma Program. I am doing a study on the air quality in Shanghai and how it has been changing over time. I am about to start my senior year so we haven't covered calculus yet, and I am kind of struggling with a normal distribution concept. I need to find the range of values for a certain percentage of the normal distribution. I know that there is a function called the probability distribution function (PDF) which can give you the percentage probability for a specific range of values, but I need the opposite. I know the percentage which is 82%, and I need to find the range of values. Is there perhaps a formula for that, or maybe a way to reverse engineer the PDF formula? I have attached the PDF formula below just in case.

 

[Dr.Peterson]

Hello, I am writing a Math IA for my IB Diploma Program. I am doing a study on the air quality in Shanghai and how it has been changing over time. I am about to start my senior year so we haven't covered calculus yet, and I am kind of struggling with a normal distribution concept. I need to find the range of values for a certain percentage of the normal distribution. I know that there is a function called the probability distribution function (PDF) which can give you the percentage probability for a specific range of values, but I need the opposite. I know the percentage which is 82%, and I need to find the range of values. Is there perhaps a formula for that, or maybe a way to reverse engineer the PDF formula? I have attached the PDF formula below just in case.

There is no "closed" algebraic formula for the Normal CDF (or for its inverse). That's why we generally either use tables or computer programs that can evaluate it approximately. Graphing calculators, spreadsheets, and statistics programs all provide this capability.