Phi- Normal Distribution (how To Look Normal Tables ) - Physics Forums

• Insights Blog -- Browse All Articles -- Physics Articles Math Articles Education Articles Bio/Chem/Tech Articles
• Forums General Math Calculus Differential Equations Topology and Analysis Linear and Abstract Algebra Differential Geometry Set Theory, Logic, Probability, Statistics MATLAB, Maple, Mathematica, LaTeX
• Trending

Log in Register What's new

• General Math
• Calculus
• Differential Equations
• Topology and Analysis
• Linear and Abstract Algebra
• Differential Geometry
• Set Theory, Logic, Probability, Statistics
• MATLAB, Maple, Mathematica, LaTeX

Menu Log in Register Navigation More options Style variation System Light Dark Contact us Close Menu You are using an out of date browser. It may not display this or other websites correctly.You should upgrade or use an alternative browser.

• Forums
• Mathematics
• Set Theory, Logic, Probability, Statistics

Phi- normal distribution (how to look normal tables )

• Context: Undergrad
• Thread starter Thread starter logicalman
• Start date Start date Dec 11, 2004
• Tags Tags Distribution Normal Normal distribution Phi

Click For Summary

Discussion Overview

The discussion revolves around how to use a normal distribution table to find values of the inverse normal function, specifically φ^-1(0.25). Participants are exploring the differences between standard normal tables and other forms of normal tables, as well as the implications of symmetry in the normal distribution.

Discussion Character

• Technical explanation
• Homework-related
• Debate/contested

Main Points Raised

• One participant seeks clarification on how to find φ^-1(0.25) using a normal distribution table, expressing frustration over the process.
• Another participant provides a detailed explanation of how to use a standard normal table, noting that it only provides positive z values and explaining the symmetry of the normal distribution.
• A third participant points out that their course uses a different type of normal table that does not include negative z values, asking for an explanation tailored to that table.
• A later reply acknowledges the difference in tables and suggests that the participant should look for z such that φ(z) = 0.25, indicating that they need to find the corresponding z value for φ(z) = 0.75 in their table.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the use of different types of normal tables and how to interpret them. There are competing views on how to approach the problem based on the type of table being used.

Contextual Notes

There is an assumption that the normal table being used by one participant is different from the standard normal table, which may lead to confusion in finding the correct values. The discussion highlights the need for clarity on the definitions and formats of the tables being referenced.

logicalman Messages 22 Reaction score 0 Phi- normal distribution (how to look normal tables!) hello, can anyone please tell me how to look up values for the following from the "normal table" distribution. \phi^-1(0.25) ans. is -0.68 but i can't figure out how the **** it is so! so please someone reply fast 'cause this simple thing is unnecessarily wasting my time! Physics news on Phys.org

• Researchers realize room-temperature two-dimensional multiferroic metal
• Inside the light: How invisible electric fields drive device luminescence
• Quantum computers must overcome major technical hurdles before tackling quantum chemistry problems

HallsofIvy Science Advisor Homework Helper Messages 42,895 Reaction score 983 A nice online table for the Normal distribution is at http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/normaltable.html To find φ-1(0.25), I would first note that the table,as shown, only gives positive values for z. That is, F(0)= 0 and F(infinity)= 0.5. The standard φ (normal function) has domain -infinity to infinity and φ(0)= 0.5. To find φ-1(0.25) then, I note that I want the area under the normal curve from -infinity to z (a negative number since 0.25< 0.5) to be 0.25. Because of symmetry, the area under the normal curve from -z (a positive number) to +infinity is also 0.25. That means that the area from 0 to -z (which is what the table gives) must be 0.5- 0.25= 0.25 also. Since I am looking for φ-1, I look in the body of the table to find the number closest to 0.25 and find that it is in the row with 0.6 on the left in the column with 0.08 at the top (actually 0.25 would be between 0.07 and 0.08) that tells me that -z= 0.68 and so z= -0.68. That can be a little misleading because of the coincidence that 0.5- 0.25= 0.25 Here's a little different problem: what is φ-1(0.3)? That is: we want to find z such that the area under the normal curve from -infinity to z is 0.3. Because of symmetry, the area from -z to infinity must also be 0.3. Since the table tells us the area under the curve from 0 to -z, we must look up the z for 0.5- 0.3= 0.2. Looking in the table, I see that closest number to 0.2, 0.1985 is in the row with 0.5 on the left and in the column headed by 0.02. -z= 0.52 so z is -0.52. φ-1(0.3)= -0.52. Last edited by a moderator: May 1, 2017 logicalman Messages 22 Reaction score 0 hi thanks for the reply, but the table in our course is a "normal table" not "standard normal" , so in my table it starts with 0.0 | 0.5. so when i look value for 0.0 i get 0.5 in the body. can you please explain in terms of the table that i am having where we don't have to add or subtract 0.5 to get the answer. thanks! instead of explain if you can use LaTex and find ans. like solving a sum would be better. once again thanks! HallsofIvy Science Advisor Homework Helper Messages 42,895 Reaction score 983 "but the table in our course is a "normal table" not "standard normal" , so in my table it starts with 0.0 | 0.5. so when i look value for 0.0 i get 0.5 in the body." Okay, I assume, then, that the only problem is that your table does not give negative z values. To find z such that &phi;(z)= 0.25, you are looking for a z such that the area under the Normal curve to the left of z is 0.25. By symmetry, this is the same as area to the right of -z. Since your table starts with &phi;(0)= 0.5 up to &phi;(infinity)= 1, it is already including the left half. You need to find z such that &Phi;(z)= 1- 0.25= 0.75. Look in the body of the table for 0.75 (or the closest number to that) and read off the corresponding z value. If &Phi;(z)= 0.75, &Phi;(-z)= 0.25.

Similar threads

High School Define if the distribution is normal or not

• Dec 18, 2018 · Replies 3 · Dec 20, 2018

Replies 3 Views 1K Undergrad Variable transformation for a multivariate normal distribution

• May 19, 2019 · Replies 1 · May 19, 2019

Replies 1 Views 2K Undergrad Finance: does the volatility of a stock follow a certain distribution?

• Feb 1, 2022 · Replies 24 · Feb 23, 2022

Replies 24 Views 4K MHB Normal and exponential distribution

• Dec 5, 2017 · Replies 5 · Dec 5, 2017

Replies 5 Views 2K Undergrad Bivariate normal distribution from normal linear combination

• Jan 8, 2019 · Replies 2 · Jan 10, 2019

Replies 2 Views 2K High School Distribution of particles, given a function

• Jun 26, 2021 · Replies 2 · Jul 2, 2021

Replies 2 Views 1K Undergrad Generating samples on a 2-D composite binomial distribution

• Oct 8, 2019 · Replies 3 · Oct 9, 2019

Replies 3 Views 1K Undergrad Understanding Distribution Notation in Calculus: Explained by PF Community

• Feb 21, 2019 · Replies 20 · Feb 25, 2019

Replies 20 Views 3K High School How Can We Compare Two Means to Test the Effectiveness of Diet A on Weight Loss?

• Nov 26, 2024 · Replies 20 · Dec 8, 2024

Replies 20 Views 3K MHB -aux04 Species of insect is normally distributed

• Jul 18, 2013 · Replies 3 · Jul 19, 2013

Replies 3 Views 6K

• Forums
• Mathematics
• Set Theory, Logic, Probability, Statistics

Hot Threads

• T

  Undergrad Please Explain (actually explain) The Monty Hall Problem

  • Started by Timbre
  • Oct 28, 2025
  • Replies: 131
  • Set Theory, Logic, Probability, Statistics
• P

  Undergrad A variant of the Monty Hall problem

  • Started by Pikkugnome
  • Nov 1, 2025
  • Replies: 9
  • Set Theory, Logic, Probability, Statistics
• W

  Graduate Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense

  • Started by WWGD
  • Dec 16, 2025
  • Replies: 4
  • Set Theory, Logic, Probability, Statistics
• M

  Undergrad My basic understanding of set theory

  • Started by mr3000
  • Dec 25, 2025
  • Replies: 20
  • Set Theory, Logic, Probability, Statistics
• 

  Undergrad How do E[X] and E[|X|] relate?

  • Started by MidgetDwarf
  • Nov 28, 2025
  • Replies: 6
  • Set Theory, Logic, Probability, Statistics

Recent Insights

• 

  Insights Remote Operated Gate Control System

  • Started by Greg Bernhardt
  • Feb 28, 2026
  • Replies: 3
  • General Engineering
• 

  Insights AI Enriched Problem Solving

  • Started by Greg Bernhardt
  • Feb 28, 2026
  • Replies: 4
  • General Math
• 

  Insights Thinking Outside The Box Versus Knowing What’s In The Box

  • Started by Greg Bernhardt
  • Oct 13, 2025
  • Replies: 27
  • Other Physics Topics
• 

  Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

  • Started by Greg Bernhardt
  • Sep 29, 2025
  • Replies: 28
  • Quantum Interpretations and Foundations
• 

  Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

  • Started by Greg Bernhardt
  • Sep 2, 2025
  • Replies: 22
  • Quantum Physics
• 

  Insights What Exactly is Dirac’s Delta Function? - Insight

  • Started by Greg Bernhardt
  • Sep 2, 2025
  • Replies: 33
  • General Math

Back Top