For a normal distribution, which of the following z−scores represents the most extreme location on the left side of the distribution?

Question

BlackTom AI · Accepted Answer

Let's restate the problem clearly: For a normal distribution, which of the following z-scores represents the most extreme location on the left side of the distribution?

Option 1: +2.17
- This is a positive z-score, meaning it lies on the right side of the distribution. Since the question asks for the leftmost extreme, a positive value does not represent the left tail, so this is not the extreme left location.

Option 2: -1.87
- This is a negative z-score, placing it in the left half of the distribution. However, among the left-side options, -1.87 is not as far into the left tail as some more negative values, so it is not the most extreme left position.

Option 3: -2.17
- This is also a negative z-score and lies farther to the left than -1.87. In a standard normal distribution, more negative z-scores correspond to locations further into the left tail, making -2.17 a stronger contender for the extreme left position.

Option 4: +1.67
- This is a positive z-score in the right half of the distribution, and thus cannot represent the left tail.

Putting these together, the leftmost extreme location among the provided options must be the most negative z-score available. Between -1.87 and -2.17, the value with the greater magnitude in the negative direction is -2.17, which places it further into the left tail than -1.87. Conversely, any positive z-scores (+2.17 or +1.67) lie on the right side and do not represent the left-tail extreme.

In summary, identifying the most extreme left position relies on recognizing that left-tail extremity corresponds to the largest magnitude of negative z-scores, i.e., the most negative value presented.

For a normal distribution, which of the following z−scores represents the most extreme location on the left side of the distribution?

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