The z-score follows a normal distribution, which is known as the standard normal distribution
The standard normal distribution, also known as the z-distribution, is a specific type of normal distribution
The standard normal distribution, also known as the z-distribution, is a specific type of normal distribution. It has a mean of 0 and a standard deviation of 1. The shape of the distribution is symmetric and bell-shaped.
The z-score is a measure of how many standard deviations an observation or data point is away from the mean of the distribution. It allows us to compare values from different normal distributions by standardizing them.
To calculate the z-score of a given value x, we use the formula:
z = (x – μ) / σ
Where:
– z is the z-score
– x is the value we want to find the z-score for
– μ is the mean of the distribution
– σ is the standard deviation of the distribution
For example, let’s say we have a normal distribution with a mean of 50 and a standard deviation of 10. We want to find the z-score for a value of 60. Plugging the values into the formula, we have:
z = (60 – 50) / 10
z = 10 / 10
z = 1
This means that the value 60 is 1 standard deviation above the mean of the distribution.
The z-score is useful in statistics and probability theory because it allows us to determine the probability of certain values occurring in a normal distribution. By looking up the z-score in a standard normal distribution table or using software, we can find the corresponding probability or percentile associated with that z-score. This can be particularly helpful in hypothesis testing, confidence intervals, and making comparisons between different data sets.
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