the area between .79 and 2.67 = .4962-.2852
= .2110
Zero.
0.1972
-0.35
One.
Look in any standard normal distribution table; one is given in the related link. Find the area for 2.43 and 1.52; then take the area for 2.43 and subtract the area for 1.52 and that will be the answer. Therefore, .9925 - .9357 = .0568 = area under the normal distribution curve between z equals 1.52 and z equals 2.43.
~0.0606
0.1972
Zero.
A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.
2
The total area under a normal distribution is not infinite. The total area under a normal distribution is a continuous value between any 2 given values. The function of a normal distribution is actually defined such that it must have a fixed value. For the "standard normal distribution" where μ=0 and σ=1, the area under the curve is equal to 1.
-0.35
One.
0.4846
It is 0.2743
0.088508
2.16