What is the standard deviation of the height distribution?

Question

BlackTom AI · Accepted Answer

The provided data shows a numerical question: 'What is the standard deviation of the height distribution?' with an answer of '2.66' and an empty list for answer_options.

Because there are no answer choices given, there is nothing to evaluate for correctness against alternative options. In a typical multiple-choice or numerical-response scenario, we would compare each option to determine which is correct; here, such comparison isn’t possible.

What we can assess is the general approach to determining the standard deviation of a height distribution if you had the underlying data or a description of the distribution:
- If you have a complete dataset of individual heights, you can compute the standard deviation by calculating the square root of the average of squared deviations from the mean.
  Steps: compute the mean (average height), subtract the mean from each height to get deviations, square these deviations, average them (or sum and divide by n for population standard deviation, or n-1 for sample standard deviation), and take the square root.
- If the problem provides summary statistics (e.g., mean and variance, or a histogram with a known distribution), you can compute the standard deviation from those values or infer it from the distribution's parameters.
- If the distribution is assumed (e.g., height is normally distributed with known parameters), the standard deviation would be a parameter of that model, which should be stated in the problem.

Because the actual data or distribution details are not present here, we cannot verify whether 2.66 is the correct standard deviation for this height distribution. The stated answer '2.66' would need to be checked against the underlying data or the distribution parameters to confirm its accuracy.

In practice, to proceed, you would either provide or obtain:
- The full height data set to compute the standard deviation directly, or
- The distribution type and its parameters (mean, variance, or standard deviation) from which you can derive the answer, or
- The summary statistics (mean and either variance or standard deviation) that allow calculation of the standard deviation.

Until such information is supplied, the correctness of the value 2.66 cannot be established from the given input.

Su25-STATS-141-01/BIO-141-01 Homework 2: Normal Distributions & Hypothesis Tests

What is the standard deviation of the height distribution?

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