Area under the standard normal curve

For what value of z is the following statement true?

P(-z<Z<z)=0.80

the solutions say 1.28 but I don't understand how they got that number

Thanks

WlND said:

For what value of z is the following statement true?

P(-z<Z<z)=0.80

the solutions say 1.28 but I don't understand how they got that number

Thanks

Click to expand...

The area under the bell curve, from z below the mean up to z above the mean, is to be 0.80.

By symmetry, the area above the mean up to z is half of that, or 0.40.

The table I use for the area under the normal curve only gives values above the mean, and the area starts at 0.50 when z=0, representing the complete left-hand side of the distribution from -infinity to 0. Since I am looking for the z that gives an area of 0.40 above the mean, I have to look for F=(0.50+0.40)=0.90. That z-value is 1.28.

If you are given this question, you certainly must have learned something about the "standard normal curve" and generally one of the first things you learn is that there is NO "analytic" method of finding the area. There are, as I assume you learned in Calculus, many numerical methods of evaluating the integral. There is probably a table of the normal distribution in your text book where you can look up that numerical integral. However, there is a very nice application at http://www.mathsisfun.com/data/standard-normal-distribution-table.html. That gives you the area from 0 to z where z is where z is the horizontal coordinate of your cursor. Since the standard normal curve is symmetric about z= 0, to find -z to z so that the area is .80, move your cursor to the z that gives "0.40" within the area.