Summary
Highlights
This section introduces the process of finding a z-score when given the area under the standard normal model using a z-table. It notes that the table primarily provides areas shaded to the left. The video also mentions that other videos cover using TI-84 and TI Inspire calculators for this purpose.
The video demonstrates finding a z-score for an area of 0.1562 shaded to the left. Since the area is less than 50%, the z-score is expected to be negative. The presenter shows how to locate this value in the z-table and determine the corresponding z-score, which is -1.01. It's noted that the table can sometimes provide approximate values.
This part explains how to find the z-score when the given area is to the right (0.1762). Since z-tables typically show area to the left, the first step is to calculate the area to the left by subtracting the given area from 1 (1 - 0.1762 = 0.8238). Because this resulting area is greater than 50%, a positive z-score is expected. The z-table lookup yields a z-score of 0.93.
The final example involves finding the negative and positive z-scores that encompass an area of 86% (0.8600) between them. The presenter explains that the remaining 14% (1 - 0.86) is split equally between the two tails, meaning 7% (0.07) is to the left of the negative z and 7% is to the right of the positive z. By looking up 0.0700 in the negative z-table, an approximate z-score of -1.48 and +1.48 is found. Alternatively, one could find the z-score for the area to the left of the positive z (0.07 + 0.86 = 0.93).