Normal distribution table values

The actual value of P(z< 0.7925) is 0.78614 so the linear interpolation is not bad.In summary, to find a value of P(Z<0.7925) from a normal distribution table with values to 2 decimal places, you can use linear interpolation between the closest values in the table. This involves finding the difference between the two closest values and then finding the fraction of that difference based on the distance from the given value to one of the closest values. This method may not be exact but can provide a close approximation.
  • #1
aurao2003
126
0

Homework Statement



Hi
I need a clarification before my S2 exam on Thursday. How do I find a value of P(Z<0.7925)? This is bearing mind that all the table values are to 2 decimal places.
Thanks.

Homework Equations


Normal Distribution Tables



The Attempt at a Solution


Previously, I have compare it to the closest value and then subtract to get my final result. For example, if I need P(Z<1.212), I would compare it to P(Z<1.21) and P(Z<1.22). Since it is closer to 1.21, I would subtract .002 from the table value. Is this method correct? I am getting a slightly different result to the questions. Please help.
 
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  • #3
aurao2003 said:

Homework Statement



Hi
I need a clarification before my S2 exam on Thursday. How do I find a value of P(Z<0.7925)? This is bearing mind that all the table values are to 2 decimal places.
Thanks.

Homework Equations


Normal Distribution Tables



The Attempt at a Solution


Previously, I have compare it to the closest value and then subtract to get my final result. For example, if I need P(Z<1.212), I would compare it to P(Z<1.21) and P(Z<1.22). Since it is closer to 1.21, I would subtract .002 from the table value. Is this method correct? I am getting a slightly different result to the questions. Please help.
Surely that's not what you meant to say! Using this table: http://www.math.unb.ca/~knight/utility/NormTble.htm [Broken]
I get that P(z< 1.21)= 0.8869 and P(z< 1.21)= 0.8888. You certainly don't want to subtract anything from P(z< 1.21) because the probability is increasing, not decreasing. And if you were to add .002, you would get 0.8908 which is already past 0.8888.

Instead, note that 0.8889- 0.8868= .0019. Since 1.212 is .2= 1/5 of the way from 1.21 to 1.22, add 1/5 of that difference: .2(.0019)= 0.00038. P(z< 1.212) will be approximately 0.8889+ .00038= 0.88728.

Similarly to approximate P(z< 0.7925), I note in the table that P(z< 0.79)= 0.7852 and P(z< 0.80)= 0.7881. That is a difference of 0.7881- 0.7852= 0.0029. 0.7925 is .25= 1/4 of the way from 0.79 to 0.80 so I find 1/4 of that difference- .0029/4= .0029(.25)= 0.000725. The linear interpolation from this table for P(z< 0.7925) is 0.7852+ 0.000725= 0.785925.

That is, as SteamKing said, a "linear interpolation"- we are assuming the graph is linear between 0.79 and 0.80 which is only approximately correct.
 
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What is a normal distribution table?

A normal distribution table, also known as a z-table, is a table that displays the probabilities for a specific range of values under a normal distribution curve. It is used to determine the probability of a certain value occurring within a normal distribution.

How do I read a normal distribution table?

A normal distribution table is read by locating the desired value in the body of the table and finding the corresponding probability in the corresponding row and column. The table is organized by the first two digits of the value, followed by the third digit in the row and the fourth digit in the column. The intersection of the row and column will give you the probability.

What is the purpose of using a normal distribution table?

A normal distribution table is used to calculate the probabilities of a certain value occurring in a normal distribution. It is commonly used in statistical analysis to determine the likelihood of obtaining a particular result or to compare a sample to the population.

What are the values in a normal distribution table?

The values in a normal distribution table represent the area under the normal distribution curve. They range from 0.00 (representing the mean) to 0.50 (representing the maximum probability).

What are the assumptions for using a normal distribution table?

The assumptions for using a normal distribution table are that the data is normally distributed, the sample size is large enough, and the values are independent of each other. Additionally, the mean and standard deviation of the distribution must be known or estimated.

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