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A Z-Score is a measurement of how many standard deviations a particular data point is from the mean. It is calculated by subtracting the mean from a particular data point (in this case already given as Z-scores), and dividing this by the standard deviation. Standard Normal Tables (also known as Z-tables) is a mathematical table that allows us to know the percentage of values below (to the left of) a z-score in a standard normal distribution. Here, since we are dealing with a normal distribution where \(\mu = 0\) and \(\sigma = 1\), our Z-score is equal to the value of z itself.

We will refer to the standard normal distribution table to find the probabilities. a. \(P(z < 0.10)\): Find the value from the standard normal table that corresponds to 0.10. That value is the probability. b. \(P(z < -0.10)\): Here, since it's a negative value, we use symmetry properties of the normal distribution which states probability of being below -0.10 is same as the probability of being above 0.10; it equals \(1 - P(z < 0.10)\). c. \(P(0.40 < z < 0.85)\): To find the probability between two values, we find the probability of lower bound and upper bound separately from the standard normal distribution table and subtract the former from the latter i.e., \(P(z < 0.85) - P(z < 0.40)\). d. \(P(-0.85 < z < -0.40)\): Similar to the previous case, we subtract the lower bound from the upper bound but as these are negative, we use the symmetry property which states probability of being below -0.85 is same as probability of being above 0.85 and likewise for -0.40. Emerges as \(P(z > 0.40) - P(z > 0.85)\). e. \(P(-0.40 < z < 0.85)\): This is calculated as \(P(z < 0.85) - P(z > 0.40)\). f. \(P(z > -1.25)\): Probability of being above -1.25 is same as probability of being below 1.25 as per symmetric property, calculated as \(P(z < 1.25)\). g. \(P(z < -1.50\) or \(z > 2.50)\): Since these are disjoint events we add the corresponding probabilities i.e., \(P(z > -1.50) + P(z < 2.50)\).