reading a table for standard normal distribution z scores

Here, the table shows and explains that the probability that a standard normal random variable will be less than -1.21 is 0.1131 i.e, P(Z < -1.21) = 0.1131. In order to find the cumulative probability of a z-score equal to -1.21, cross-reference the row containing -1.2 of the table with the column holding 0.01. The cumulative probability (from –∞ to the z-score) are visible in the cell of the table.įor instance, a part of the standard normal table has been given below. The columns of the standard normal distribution table represent the hundredth place. The rows of the standard normal distribution table represent the whole number and tenth place of the z-score. This is known as area Φ.Ī standard normal distribution table basically displays a cumulative probability linked with a particular z-score. If one has to discover the probability of a value that is not exactly or more than a fixed positive z value, it can be found out by a standard normal distribution table. Since its shape looks like a bell, the normal distribution density function f(z) is called the Bell Curve. It is applicable for only positive values of z.Ī standard normal distribution table comes into use to determine the area under the bend (f(z)) to find out the probability of a specific range of distribution. The normal distribution, also known as Gaussian distribution, is a persistent probability distribution. The standard normal distribution table is used to calculate the probability of a regularly distributed random variable Z, whose mean is 0 and the value of standard deviation equals 1. A narrow curve is produced by a small standard deviation while a wide curve is produced by a large standard deviation. The curve is stretched by the standard deviation. The curve travels right when the mean is increased and left when the mean is decreased. The curve centre is determined by the mean. Every normal distribution is a stretched or squeezed variant of the standard normal distribution that has been moved horizontally right or left. In a typical normal distribution, the mean and standard deviation are always fixed. Whereas the normal distribution on the other hand can have any mean and standard deviation. The standard normal distribution is unimodal and symmetrically distributed with a bell-shaped curve. Normal Distribution VS Standard Normal Distribution

Read More: Mean and Variance of Random Variable The following formula can be used to convert any normal random variable X into a z score:

The random variable of a standard normal curve is referred to as the standard score or a Z-score. Standard Normal Distribution is a kind of normal distribution that appears when a normal random variable has a mean value equals to zero and the value of standard deviation equals one.

Reading a table for standard normal distribution z scores