Hi there,

I feel that the above did not exactly answer your question as it looks more like you are having a hard time visualizing what z-values represent.

Let me try to do my best.

First, realize that the z-score is nothing but a standard deviation from zero (that is , the mean of the standard normal distribution).

Second, the number that the z-value points at when we look at the table is the Probability that everything else lies BELOW that point.

Now, thing of the bell shape. If you shade the whole shape all the way to the right you have a probability of 1 that everything lies behind (on the left ) of that point. You will see that the z-score that goes close to giving us the probability one is close to 3.49. All that means is that if you multiply the Standard deviation (which is one for the standard normal) by 3.49 times you are going far enough to the right to consider everything else lying below it / to the left.

Having that down let’s see what the problem said:

You find a value that shows 90.32% probability that everything is on the left. However, notice that the safety first talks about the OTHER side of the bell curve. You want to know what is beneath 1.3 standard deviations to the left, not to the right as you are currently doing.

Now the thing with the standard normal is that it is SYMMETRICAL. That means that whatever lies 1.3 times to the left, also mirrors , 1.3 times to the right.

Since the total bell covers an area of 1. And since you essentially “shaded” all the area to the **positive** 1.3 deviations, what you need to do to “see” on the other side of the curve subtract from unity the shaded area that you are currently looking at. What you will be left with is the probability that something lies either : OVER 1.3 deviations or UNDER 1.3 deviations.

I know this can be tricky the first time, but I hope I helped out.

EDIT : To aid your understanding , please look at the table here http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

The top table represents z values on the left side of the mean. The probabilities always show how much area lies to the left of that.

The bottom tables represents z values on the right side of the mean. Again the probabilities show how much area lies to the left.

That is why you can always arrive at the first table by doing 1 minus z-value.

Some people get confused thinking that the probabilities under the positive z-scores cover the area to the right. This is wrong. The probabilities ALWAYS show how much is to the left of that point.

EDIT2: Even more help here : http://www.youtube.com/watch?v=mai23vW8uFM&feature=related

Good luck!