In a certain school district in a large metropolitan area, the SAT scores over that past five years are normally distributed with a mean of 1476. Furthermore, P20
is 1209.
For a normal distribution, what is the z-score for the 20-th percentile?
To find the z-score for the 20th percentile (P20), we need to refer to the standard normal distribution (Z-table). The 20th percentile means that 20% of the data falls below this point.
Standard normal distribution tables reflect the area under the curve to the left of a z-score. To find the z-score corresponding to P20 or the 20th percentile, we need to look up the value in the Z-table that is closest to 0.20.
Upon consulting the Z-table, we find that the z-score corresponding approximately to the 20th percentile (0.20 area to the left) is -0.84. This means that a score at the 20th percentile is 0.84 standard deviations below the mean.
Therefore, the z-score for the 20th percentile for this SAT scores distribution is approximately -0.84.