# Normal Distribution/Z-table usage

• June 9th 2008, 01:04 PM
trackies
Normal Distribution/Z-table usage
Hi there!

I've been really perplexed by this for the past hour or so, so I'd really appreciate it if you could help me.

So I have this:

0.5 - P(0 < Z < 0.6667)
= 0.5 - 0.2475
= 0.2525

I don't understand how P(0<Z<0.6667) was solved. How do I find 0.6667 in the Z-table, as it only goes to two decimal places? I've been stumped every time I come across a number with three or more decimal places.

NB. The Z-table that has been provided to us only goes up to 0.9 at the top and 3.0 down the side, hence my confusion.
• June 9th 2008, 02:13 PM
mathceleb
Quote:

Originally Posted by mr fantastic
I have no time now but will reply later if no-one else does.

Probability of a Random Variable in the Normal Distribution

Press the appropriate probability button, in this case, the third one, and Enter 0 and .667 and press the Calculate button. It will show you the math.

Now, for an in depth description. The normal distribution follows a bell curve, the theory being, that 1/2 of all possible cases rests at 0, based on a Z score which is (X - mu)/sigma.

With respect to your table, everybody works differently. I have a book that uses 2 decimal places. For you, I'd round and look for 0.67. If you want to split hairs, you can interpolate between 0.66 and 0.67 if you are familiar with interpolation.

Or, use Excel for exact decimals: =NORMSDIST(0.667)-NORMSDIST(0)
• June 9th 2008, 02:21 PM
Moo
Hello,

Quote:

Originally Posted by mathceleb

Probability of a Random Variable in the Normal Distribution

Press the appropriate probability button, in this case, the third one, and Enter 0 and .667 and press the Calculate button. It will show you the math.

Now, for an in depth description. The normal distribution follows a bell curve, the theory being, that 1/2 of all possible cases rests at 0, based on a Z score which is (X - mu)/sigma.

With respect to your table, everybody works differently. I have a book that uses 2 decimal places. For you, I'd round and look for 0.67. If you want to split hairs, you can interpolate between 0.66 and 0.67 if you are familiar with interpolation.

Or, use Excel for exact decimals: =NORMSDIST(0.667)-NORMSDIST(0)

If you read a table normally, you can see that $P(0, which means that it hasn't been rounded.
• June 9th 2008, 06:22 PM
trackies
Thank-you so much for your replies! My friend was online briefly and explained interpolation to me, so I managed to use that.
• June 10th 2008, 12:28 AM
CaptainBlack
Quote:

Originally Posted by trackies
NB. The Z-table that has been provided to us only goes up to 0.9 at the top and 3.0 down the side, hence my confusion.

If you re-examine your table you will find it goes to 3.0 in steps of 0.1 downwards, and from 0.00 to 0.09 in steps of 0.01 accross.

To look up z=0.6667 look up z=0.66 and z=0.67, the value you seek is 2/3 of the way between the tabulated values just looked up.

RonL