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Z-scores are a way of describing a data point's position in relation to the mean of a group of data points, in terms of standard deviations. Essentially, a z-score tells you how many standard deviations away from the mean a particular score is. For instance, if we have a positive z-score, it indicates that the data point is above the mean, and a negative z-score indicates it is below the mean.

In the context of the exercise, when we compute the z-scores of -2.75 and -1.28, we see that both numbers are negative, placing both points below the mean on a standard normal distribution curve. By looking up these z-scores in the standard normal table, we can find the proportion of the data that lies between these values and the mean.

Cumulative probabilities are used to determine the likelihood that a variable will take on a value less than or equal to a certain point. In the realm of statistics, this is often visualized on the normal distribution curve. When dealing with standard normal distribution, cumulative probabilities correspond to the area under the curve to the left of a given z-score.

This concept allows us to perform calculations like those needed in the given exercise, where we find the cumulative probabilities for each of the z-scores -2.75 and -1.28. The difference between these two probabilities then gives us the area between these two points on the curve, which is exactly what we need to solve our problem.

Normal distribution, often known as the bell curve due to its shape, is a continuous probability distribution that is symmetrical around its mean, meaning most data points cluster around the mean. The standard normal distribution is a special case of the normal distribution, where the mean is 0 and the standard deviation is 1.

The area under the standard normal curve represents the probability of a score falling within a particular range. The exercise provided is a classic example involving the standard normal curve, where we're looking for the area between two points on the curve. This area corresponds to the probability that a randomly selected score from a normally distributed population falls between those two z-scores, effectively quantifying the notion that the majority of values are close to the mean in a normal distribution.