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Understanding the concept of standard deviation is crucial when dealing with any form of data that varies. It measures how spread out the numbers in a data set are. In a more technical term, standard deviation is the average distance from the mean of the data set. A small standard deviation indicates that the values in a data set are close to the mean of the data set, while a large standard deviation indicates that the values are spread out over a wider range.

Regarding the z score calculation exercise, knowing the standard deviation allows us to determine how far a particular reading speed is from the average speed, which is essential for finding the z score. If a student reads at 320 wpm, and the standard deviation is 70 wpm, this means the student's speed is more than one standard deviation below the average. Recognizing this helps to contextualize the student's performance.

The concept of normal distribution, often referred to as the 'bell curve', is a foundational idea in statistics. It represents a distribution where most of the data points cluster around a central point, known as the mean, with values tapering off symmetrically on both sides as they move away from the mean.

In terms of our exercise, the reading speeds of students are likely to follow a normal distribution, assuming a large and random sample of students. This is important because the z score calculation assumes that the distribution of the variable (reading speed, in this case) is normal. Under a normal distribution, specific z scores correspond to percentages that represent the likelihood of observing a value at or below a given point; an important concept in statistical analysis and interpretation of the z score.

Statistical analysis involves collecting, reviewing, and interpreting data to discover underlying patterns and trends. It is an essential tool for making informed decisions based on quantitative data. In our z score exercise, statistical analysis would involve examining how different reading speeds compare to the average reading speed once the z scores are calculated.

By calculating the z score, we can perform a statistical analysis to identify how individual students' reading speeds differ from the average or expected speed. A z score tells us how many standard deviations an observation is from the mean, which is critical information in understanding whether a reading speed is typical, exceptionally high, or low. This information can be used to assess students' progress and even tailor instruction to improve reading skills.