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he heights of one hundred trees in a certain forest are measured. It’s found that the mean height of the trees is 48 feet. Use this information to answer the following:
Would it be possible to have a standard deviation of 7.5 feet? If so, what would this tell us about the tree heights in the forest?
Would it be possible to have a standard deviation of 1? If so, what would this tell us about the tree heights in the forest?
Would it be possible to have a standard deviation of 0? If so, what would this tell us about the tree heights in the forest?
Would it be possible to have a standard deviation of -2.5? Why or why not?

Respuesta :

Using the concept of standard deviation, it is found that:

  • It would be possible to have standard deviations of 7.5 feet and 1 feet, which would mean that the distribution of tree heights are normal.
  • It would be possible to have a standard deviation of 0 feet, which would mean that all trees have the same height.
  • It would not be possible to have a standard deviation of -2.5 feet, as it is always a positive value.

  • The standard deviation of a data-set is given by the square root of the sum of the differences squared of each observation and the mean, divided by the one less than the number of values.
  • It is always a positive value, thus, a standard deviation of -2.5 feet, for example, is not possible.
  • If a data-set has a standard deviation of 0, it means that all values in the data-set are the same.

In a normal distribution, 99.7% of the measures are within 3 standard deviations of the mean.

[tex]48 \pm 3(7)[/tex] and [tex]48 \pm 3(1)[/tex] are both reasonable distributions for the tree heights, thus, it is possible to have standard deviations of 7.5 and 1 feet.

A similar problem is given at https://brainly.com/question/24754716

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