Transcript American - Humble ISD

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?
9  11.2
z
 ̶ 1.07
2.06
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?
17  11.2
z
 2.82
2.06
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?
12  11.2
z
 .39
2.06
14  11.2
z
 1.36
2.06
P(12 < x < 14) = .2618
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
11.2
x
x  11.2
z
2.06
x  11.2
1.04 
2.06
x = 13.34 feet
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