The Normal Distribution

Lake Maggiore, St. Petersburg, Florida

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?

06.2

2.119z ̶/

1.07

P(x < 9) = .1428

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?

06.2

2.1117z 2.82

P(x > 17) = .0024

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?

06.2

2.1112z .39

P(12 < x < 14) = .2618

06.2

2.1114z 1.36

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?

06.2

2.11x

z

x = 13.34 feet11.2

.1511.2

1.042.06

x

x

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)

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?

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?

END