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The z-table is a table that provides probabilities (areas) associated with the standard normal distribution. The table shows the area to the LEFT of given z-scores. The table is divided into two parts: the positive z-score table and the negative z-score table. They both have the same areas but in different directions. The positive z-table gives you an area to the LEFT of z, while the negative z-table tells you about the area to the RIGHT of z.

When looking for the area between z=0 and z=1.95, consult the positive z-table because the z-score is positive. The area under the curve from z=0 to z=1.95 can be found by looking up the area corresponding to z=1.95 in the z-table, which is 0.9744.

When looking for the area between z=0 and z=-2.05, consult the negative z-table because the z-score is negative. The area under the curve from z=0 to z=-2.05 can be found by looking up the area corresponding to z=-2.05 in the z-table, which is 0.0202.

When looking for the area between z=1.15 and z=2.37, consult the positive z-table because the z-scores are positive. But this time you need to look up separate z-scores and subtract their corresponding areas to find the area under the curve between these two points. The area under the curve from z=1.15 to z=2.37 can be found by subtracting the area corresponding to z=1.15 (0.8749) from the area corresponding to z=2.37 (0.9911). So, the area is 0.9911 - 0.8749 = 0.1162.

When looking for the area between z=-1.53 and z=-2.88, consult the negative z-table because the z-scores are negative. Similarly to step 4, look up separate z-scores and subtract their corresponding areas. The area under the curve from z=-1.53 to z=-2.88 can be found by subtracting the area corresponding to z=-1.53 (0.0625) from the area corresponding to z=-2.88 (0.0020). So, the area is 0.0625 - 0.0020 = 0.0605.

When looking for the area between z=-1.67 and z=2.24, which span both negative and positive z-scores, consult both the negative and positive z-tables. For the area at the negative z-score, look at the area to the RIGHT of z=-1.67, and for the positive z-score, look for the area to the LEFT of z=2.24. Then, add these two areas together. The area under the curve from z=-1.67 to z=2.24 can be found by adding the area corresponding to z=-1.67 (0.0475) and the area corresponding to z=2.24 (0.9875). So, the area is 0.0475 + 0.9875 = 1.035. However, the total area under the normal curve cannot exceed 1. It means that these two areas overlap. We need to subtract the overlapped part, which is the area to the left of z=0 in the positive z-table, from 1. The result is 1 - 0.5 = 0.5.