Confused with the z-score and the value x in the normal distribution? Let's figure it out

 In this week's study, I found that the R functions qnorm() and pnorm() are sometimes confused with the z-score and the value x in the normal distribution. It is important to understand the differences between these concepts to use them correctly in statistical analysis. The z-score is a standardized score that represents the number of standard deviations a data point is from the mean of a normal distribution. The z-score is calculated as: z = (x - μ) / σ  , where x is the data point, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

On the other hand, the qnorm() function in R is used to calculate the inverse of the cumulative distribution function of the normal distribution, known as the quantile function. The qnorm() function returns the z-score that corresponds to a given percentile or probability in a normal distribution with a specified mean and standard deviation. Similarly, the pnorm() function in R calculates the cumulative distribution function of the normal distribution. The pnorm() function returns the probability that a random variable from a normal distribution with a specified mean and standard deviation is less than or equal to a specified value x. While these concepts are related, they are not interchangeable. It is important to understand which concept you are working with and use the appropriate function or formula to calculate the desired value.