One.
0.1972
A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.
The area under N(0,1) from -1 to 1 = 0.6826
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.
Yes, and is equal to 1. This is true for normal distribution using any mean and variance.
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.
~0.0606
0.1972
The constant 1/sqrt(2pi) in the formula for the standard normal distribution is significant because it normalizes the distribution so that the total area under the curve equals 1. This ensures that the probabilities calculated from the distribution are accurate and meaningful.
Yes, it is true; and the 2 quantities that describe a normal distribution are mean and standard deviation.
0.4846
A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.
2.16
The distribution of sample means will not be normal if the number of samples does not reach 30.
The area under the standard normal curve is 1.
The Z value is negative, but area is always positive.
The area under N(0,1) from -1 to 1 = 0.6826