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Nadya [2.5K]
3 years ago
8

In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fah

renheit (°F). Approximately 95% of all daily high temperatures are between 83°F and 89°F. What is the standard deviation of the distribution?
Advanced Placement (AP)
1 answer:
Sonbull [250]3 years ago
6 0

Answer:

  • <u><em>The standard deviation of the distribution is 1.5ºF.</em></u>

Explanation:

The known 68-95-99.7 rule, the empirical rule, states that, in a normal distribution 68% of the data are within one standard deviation from the mean, 95% of the data are within two standard deviations from the mean, and 99.7% are within three standard deviations:

  • 68% ⇒ mean ± 1 standard deviation
  • 95% ⇒ mean ± 2 standard deviations
  • 99.7% ⇒ mean ± 3 standard deviation.

Hence, for the<em> approximately normal distribution of the daily high temperatures</em>,<em> with mean 86º</em>, and a range of <em>83ºF to 89ºF</em> for <em>95% of the data,</em> you can write:

  • 86ºF ± 2 SD ⇒ 86ºF - 2 SD = 83ºF, and

  • 86ºF ± 2 SD ⇒  86ºF + 2SD = 89 ºF

Both equations will lead to the same result:

  • 86ºF - 2 SD  = 83ºF ⇒ 2 SD = 86ºF - 83ºF = 3ºF

         SD = 3ºF / 2 = 1.5ºF

Also:

  • 86ºF + 2SD = 89ºF ⇒ 2 SD = 89ºF - 86ºF = 3ºF

         SD = 3ºF / 2 = 1.5ºF

Therefore, the standard deviation of the distribution is 1.5ºF.

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