LOCATING PERCENTILES UNDER THE NORMAL CURVE || GRADE 11 STATISTICS AND PROBABILITY Q3

The video introduces percentiles as measures of relative standing, describing how a measurement relates to the rest of the data. For instance, being in the 90th percentile means 90% of scores are lower than yours and 10% are higher. It also reminds viewers that to find the Z-value from an area, one must locate the area in the body of the Z-table and then find the corresponding Z-score.

The first example demonstrates how to find the Z-score for the 90th percentile. The 90% area is split into 0.5 (half of the normal curve) and 0.4. The closest area to 0.4 in the Z-table is 0.3997, which corresponds to a Z-score of 1.28. Thus, the 90th percentile has a Z-score of 1.28.

The video moves on to finding the Z-score for the 96th percentile. Similar to the previous example, the area is split into 0.5 and 0.46. The nearest value in the Z-table to 0.46 is 0.4599, which corresponds to a Z-score of 1.75. Therefore, the Z-score for the 96th percentile is 1.75.

This section explains how to find the Z-score for the upper 10% of the normal curve. Since it's the upper portion, we subtract 0.10 from 0.5 (half of the curve), resulting in 0.40. The closest area to 0.40 in the Z-table is 0.3997, giving a Z-score of 1.28. So, the upper 10% is above a Z-score of 1.28.

An example is provided to calculate the percentile rank of a score of 84, given a mean of 80 and a standard deviation of 15. First, the raw score of 84 is converted to a Z-score using the formula (X - mean) / standard deviation, yielding 0.27. The area corresponding to 0.27 in the Z-table is 0.1064. Since the score is positive, 0.5 is added to this area, resulting in 0.6064, which means the percentile rank is 60.64%.

The final example focuses on finding the minimum grade needed to be in the top 10% of a class, given a mean of 70 and a standard deviation of 12. Similar to previous examples, the Z-score for the top 10% is 1.28. Using the formula X = Z * standard deviation + mean, the minimum grade is calculated as (1.28 * 12) + 70, which equals 85.36 or approximately 85.