# Thread: Interpolating Normal Distribution Table

1. ## Interpolating Normal Distribution Table

Hello all,

What is to be done when determing z-values and probabity when the given value doesnt have a clean answer. For example: What is the value of z for a probability of 0.700. The table gives z
of 0.524 to be 0.699. Should I go up to 0.525 (which gives 0.7002)
or stay at 0.524.

Also 0.9981 has a range of z from 2.90 to 2.99. What value should be
used?
The book I am using says just obtain Fi(z)= p by
interpolating. Nothing fancy though. Yet I'm having lots of problems
like the ones below.

The random variable Z~N(0,1). Find the value of u.
P(Z>u) = 0.0071 As the table only gives positive z values, this
becomes.
P(Z<=u) = 0.9929. The book says to look for a value of z for Fi(z)
=0.9929. However the value that it gives is 2.452 even though 2.450
also gives the same answer. To me this makes sense as you want the
highest value that gives the required probability. But the book says
to intepolate if the value of p is between to values of z.
Next example,
P(Z>u)=0.9977. The range of values of Fi(z) is -2.847 to -2.828 and
the answer given is -2.834. Why?

Thanks a lot.

2. Originally Posted by woollybull
Hello all,

What is to be done when determing z-values and probabity when the given value doesnt have a clean answer. For example: What is the value of z for a probability of 0.700. The table gives z
of 0.524 to be 0.699. Should I go up to 0.525 (which gives 0.7002)
or stay at 0.524. Mr F says: I'd go with the value of z that gave the closest answer to 0.7000, that is, 0.524 (especially since I know that, correct to four decimal places, it's 0.5244 )

Also 0.9981 has a range of z from 2.90 to 2.99. What value should be
used? Mr F says: Correct to four decimal places, the value is 2.8943 ......

The book I am using says just obtain Fi(z)= p by
interpolating. Nothing fancy though. Yet I'm having lots of problems
like the ones below. Mr F says: In this day and age of technology, there are better things to be having lots of problems with than interpolating from a set of tables. The simplest approach is to just take a linear interpolation between the two numbers.

The random variable Z~N(0,1). Find the value of u.
P(Z>u) = 0.0071 As the table only gives positive z values, this
becomes.
P(Z<=u) = 0.9929. The book says to look for a value of z for Fi(z)
=0.9929. However the value that it gives is 2.452 even though 2.450
also gives the same answer. To me this makes sense as you want the
highest value that gives the required probability. But the book says
to intepolate if the value of p is between to values of z. Mr F says: 2.452 is the correct answer, to three decimal places. The midpoint is 2.451 ......

What you're experiencing is one of the problems when using tables to find 'extreme' values ......

Next example,
P(Z>u)=0.9977. The range of values of Fi(z) is -2.847 to -2.828 and
the answer given is -2.834. Why? Mr F says: I think either you've read your tables wrong or your tables are wrong. According to >my< tables, the range of values of u will be -2.838 to -2.830 ...... The correct answer, to four decimal places, is -2.8337. To three decimal places it's -2.834, midway between -2.838 and -2.830 ....

Thanks a lot.
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### normal distribution by interpolation with example

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