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The Normal Distribution

This document explores the normal distribution of alligator sizes, focusing on American and Chinese alligators. The mean length of an adult male American alligator is 11.2 feet with a standard deviation of 2.06 feet. Statistical analyses reveal proportions of alligators measuring below or above specific lengths, such as the likelihood of an alligator exceeding 17 feet or identifying the cutoff length for the largest 15% of the population. Additionally, we examine the endangered status of the Chinese alligator, with a mean length of 5 feet, highlighting conservation implications.

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The Normal Distribution

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  1. The Normal Distribution Lake Maggiore, St. Petersburg, Florida

  2. Alligators are only native to the United States and China. The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet and an approximately normal distribution. What proportion of adult males are less than 9 feet? ̶ 1.07 P(x < 9) = .1428

  3. The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet. The largest alligator recorded in Florida was 17.4 feet. What is the probability an adult male alligator is more than 17 feet? 2.82 P(x > 17) = .0024

  4. The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet. What is the probability an adult male alligator is between 12 and 14 feet long? .39 1.36 P(12 < x < 14) = .2618

  5. The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet. What is the cut off length for the largest 15% of American alligators? .15 x 11.2 x = 13.34 feet

  6. In China, the alligator is extremely endangered and can only be found along the Yangtze River. The average length of the Chinese alligator is 5 feet with a standard deviation of 0.67. Chinese legend says that the largest Chinese alligator was measured to be 10 feet long. The largest alligator recorded in the U.S. was an alligator from Louisiana that measured 19 feet 2 inches. N(11.2, 2.06)

  7. In China, the alligator is extremely endangered and can only be found along the Yangtze River. The average length of the Chinese alligator is 5 feet with a standard deviation of 0.67. Chinese legend says that the largest Chinese alligator was measured to be 10 feet long. The largest alligator recorded in the U.S. was an alligator from Louisiana that measured 19 feet 2 inches. N(11.2, 2.06) Which alligator measures to be in the highest percentile for their country?

  8. Chinese: 10 feet N(5, .67) American: 19 feet 2 inches N(11.2, 2.06) Which alligator measures to be in the highest percentile for their country?

  9. END

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