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Interpolating stats tables

Y

yeah_baby

Member
Does anyone know...

When using the Standard Normal table to look up probabilities is it necessary to interpolate? The solutions in the Q&A Bank seem to do so. But under exam conditions, if I'm pushed for time I'd rather just go with the rounded figure if it makes no odds to the examiners.

And if it is required, how far is it required e.g. looking up P(Z<1.2345), is

0.6*P(Z<1.23) + 0.4*P(Z<1.24)

sufficient? Or do we need to go to

0.55*P(z<1.23) + 0.45*P(Z<1.24)?

And do we need to write down what we did? (Writing them out takes ages!)

This has turned into quite a long post for a simple question - but not knowing whether to do it or not makes me so nervous every time I do one of these questions!
 
I think it depends upon the actual question you are doing...

If for example, you have estimated the distribution using a normal distribution, (say approximating a binomial with a normal) then I wouldn't interpolate if I ended up needing P( Z > 1.2345 )

But if it was a question say with X ~ N( m, sigma) then I would interpolate, you can always leave it, and then go back if you have time
 
Afraid

you have to use the exact figures, the solutions always do. Practice it and it will become easier - no need to show how you got it though, the final answer would suffice. You're gonna need this for later exams as well, so better familiarise yourself with this now without stressing to make the future easier for yourself.

Good luck
 
Or use a calculator

Both replies are excellent!

However, you could always buy a calculator that works out normal probabilities for you - then (providing you type in the full figure) it'll do the interpolation for you.

Calculators that do this are:

Casio FX991-ES
Casio FX570-ES
(not a chance for FX-83 or FX-85 !)

Sharp EL520WB
Sharp EL530VB
Sharp EL506WB
(but not the Sharp EL531WB!)

Given that it's close to the exam and using a new calculator in the exam would be bad - simply use it for the interpolation only.

Cheapest place seems to be Argos.
 
Hi

Since we can no longer use our calculators to work out the normal distribution, can someone please tell me if there is an easier way to interpolate.

eg. Qu 2 April 2008 part b

The examiners do the following:

= 1 - Φ(0.930645)
= 1 - (0.9 x 0.82381 + 0.1 x 0.82639)

how can you justify using the 0.9 and 0.1 - is to 1 decimal place sufficient enough? :confused:

thanks
 
Hello Alias

I don't think there is an easy way round this I'm afraid!

The examiners here are really interpolating to 3 dps (you've already got 0.93 and 0.94 in the tables). I think this should be ok for most uses but I'd suggest it's not really much extra work to interpolate using the exact value so if I were in the exam I'd have probably gone for this approach.

It doesn't actually make much difference here - 0.8240 vs 0.8241 for the interpolated value under the two approaches.

Hope this helps - good luck with the exam tomorrow!
 
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