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Cumulative proportions?

EG.

μ=60, σ=14, x=76

z=x-μ/ σ

=76-60/14

=1.14

I rounded off z=1.14 to the nearest z (1.15)

And found the cumulative proportion of z by looking at a random number table, and the value I found in the random number table was 0.8749.

BUT!!! the 'Solutions' stated that the value was 0.87493, which I'm assuming was figured out by hand. Does anyone know how this cumulative proportion was calculated (if it's possible to calculate cumulative proportion by hand)?

1 Answer

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    No, you cannot figure it out by hand.

    You could use a different standard normal distribution

    table sometimes called a z table

    { table IS NOT A RANDOM NUMBER TABLE}

    or you could use Microsoft Excel

    where you use

    =normdist(1.15,0,1,1)

    The format of Excel's normdist function is

    =normdist(z,µ,σ,1)

    of course z is the observed z

    With z tables, µ is always 0 and σ is always 1

    and the second 1 is to indicate that it is the actual

    Cumulative proportion, not simply the ordinate of

    the normal distribution{height of density function}

    You will allways need that 1 so

    use

    =normdist(z,0,1,1)

    You cannot do this by hand because the formula for

    the normal distribution is EXTREMELY unwieldy, you need

    computers or calculators(or tables). By hand, one would

    use some long numerical methods.

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