Question

Alligators captured in Florida are found to have a mean length of 2 meters and a standard deviation of 0.35 meters. The lengths of alligators are believed to be approximately normally distributed. What is the approximate length of an alligator at the 67th percentile of alligator lengths?

a. 2.01 meters.
b. 2.44 meters.
c. 2.21 meters.
d. 2.15 meters.
e. 2.09 meters.

Answer 1

Answer:

The correct option is (d). 2.15 meters.

Step-by-step explanation:

According to the given scenario, the approximate length of an alligator at the 67th percentile is as follows:

The length of an alligator is $X \sim N(2,0.35)$ .

Let us assume the $P_{67}$ be the 67th percentile

$P(X <P67) = 0.67\\\\P(Z < \frac{P_{67 - 2 }}{0.35} ) = 0.67\\\\\emptyset (\frac{P_{67 - 2 }}{0.35} ) = 0.67\\\\ (\frac{P_{67 - 2 }}{0.35} ) = \emptyset^{-1 (0.67)$

$\frac{P_{67 - 2 }}{0.35} = 0.44\\\\P_{67} = 2.154$

Hence, the correct option is (d). 2.15 meters