Phi- normal distribution (how to look normal tables )

In summary: For example, in the row with 0.7 on the left, the first column is 0.04 and the last is 0.09. Since 0.75 is between those, we can read off z= -0.52 as the closest value. That is, Φ-1(0.75)= -0.52.
  • #1
logicalman
22
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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.

[tex] \phi^-1(0.25) [/tex]


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!
 
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  • #2
A nice online table for the Normal distribution is at
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/normaltable.html [Broken]

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.
 
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  • #3
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!
 
  • #4
"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.
 

1. What is the Phi-normal distribution?

The Phi-normal distribution, also known as the standard normal distribution, is a specific type of normal distribution with a mean of 0 and a standard deviation of 1. It is often used in statistics to model continuous data that follows a bell-shaped curve.

2. How do I determine the probability of a specific value in a Phi-normal distribution?

To determine the probability of a specific value in a Phi-normal distribution, you can use a normal distribution table, also known as a Z-table. This table provides the cumulative probability for different Z-scores, which represent the number of standard deviations away from the mean.

3. How do I use a normal distribution table to find probabilities?

To use a normal distribution table, you first need to calculate the Z-score for the value you are interested in. Then, find the corresponding Z-score in the table and read the corresponding probability. Keep in mind that the table only provides probabilities for positive Z-scores, so you may need to use the complementary rule to find the probability for negative Z-scores.

4. Can I use a normal distribution table for any normal distribution?

No, normal distribution tables are only applicable for Phi-normal distributions with a mean of 0 and a standard deviation of 1. If you have a different normal distribution, you will need to standardize it first by subtracting the mean and dividing by the standard deviation before using the table.

5. How do I interpret the probabilities from a normal distribution table?

The probabilities in a normal distribution table represent the area under the curve up to a specific Z-score. This means that the probability of a value falling within a certain range is equal to the difference between the probabilities for the two Z-scores that define that range. For example, if the probability for a Z-score of 0.8 is 0.7881 and the probability for a Z-score of 0.9 is 0.8159, then the probability of a value falling between 0.8 and 0.9 is 0.8159 - 0.7881 = 0.0278.

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