To find the z score associated with the 74th percentile of a normal distribution, we refer to the standard normal distribution table (z table) or use statistical software.
The 74th percentile means that 74% of the data falls below this value. In a standard normal distribution (mean of 0 and standard deviation of 1), a z score corresponds to the area under the curve to the left of that score.
Looking up the cumulative probability of 0.74 in the z table or calculating it through software, we find that the z score is approximately 0.64. This means that a z score of 0.64 is the point at which 74% of the data falls below it in a standard normal distribution.