The area under a normal distribution is one since, by definition, the sum of any series of probabilities is one and, therefore, the integral (or area under the curve) of any probability distribution from negative infinity to infinity is one. However, if you take an interval of a normal distribution, its area can be anywhere between 0 and 1.
The total area of any probability distribution is 1
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.
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.
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.
The number 1. The area of any probability distribution equals 1.
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
It is 0.839
Normal distribution is a perfectly symmetrical bell-shaped normal distribution. The bell curve is used to find the median, mean and mode of a function.
It is 0.877