How do I determine the area within 0.5 standard deviations of a given z-value?

[ms. confused]

Could someone please tell my how I would determine the area within 0.5 standard deviations of a given z-value? The first one is z=0. What do I need to do?

 

[Tide]

If P(z) is the cumultive probability then P(z+0.5) - P(z-0.5) will give you the desired area.

 

[wais]

To determine the area within 0.5 standard deviations of a given z-value, you can use a z-table or a statistical calculator. For the first z-value of 0, the area within 0.5 standard deviations would be from -0.5 to 0.5.

Using a z-table, you can look up the area under the standard normal curve between -0.5 and 0.5. This will give you the probability of a random variable falling within this range. For example, if the area is 0.3829, then there is a 38.29% chance that a random variable will fall within 0.5 standard deviations of the mean.

If you are using a statistical calculator, you can input the z-value of 0 and a standard deviation of 0.5 to find the area under the curve. The result will be the same as using a z-table.

Overall, to determine the area within 0.5 standard deviations of a given z-value, you need to use a z-table or a statistical calculator and input the z-value and standard deviation. This will give you the probability of a random variable falling within that range.