Using the invNorm Function

1.645
and a standard deviation (also called the standard error): For the standard normal distribution, P(-1.96 < Z < 1.96) = 0.95, i.e., there is a 95% probability that a standard normal variable, Z, will fall between -1.96 and 1.96….Confidence Intervals.

1 Expert Answer The answer is lower z=-1.645 and upper z = 1.645 the normal curve is symmetric.

To get the area between two z- scores, tell Excel to subtract The area to the left of the higher z-score, minus the area to the left of the lower z-score.

How to find area left of a z score: Steps

1. Press 2ND and then VARS to display the DISTR menu. Select 3 and press ENTER to bring up the invNorm wizard screen.
2. Enter the desired percentile as a decimal next to the word area.
3. Press Enter again, and the TI-84 Plus will calculate the z-score associated with the chosen percentile.

For areas between two z-values, say z0 and z1 (where z0 < z1): find the area to the left of z1 and subtract from it the area to the left of z0. This is a slightly more challenging task than calculating an area, because you basically work “backwards” from an algebraic standpoint.

The majority of these methods report the area to the left of the specified z-score z, no matter where it lies. This comes from a calculus operation of integration, which finds an area from the start of a distribution (i.e., the far left-tail) up to the z-score. Two images are provided.

Example 6.1: Calculating and Graphing z-Values Given a normal distribution with μ = 48 and s = 5, convert an x -value of 45 to a z -value and indicate where this z -value would be on the standard normal distribution. Begin by finding the z -score for x = 45 as follows.

Some teachers require students to use z-tables, but there are other ways to find area under the normal curve. You may have a calculator with a normal cumulative distribution function (normalCDF) like the TI 84. Even better, try the fantastic Normal CDF calculator here!