Question

The average height of adult giraffes in a wildlife preserve is 16.5 feet, with a standard deviation of 1.3 feet. What is the probability that a randomly selected giraffe will be shorter than 18 feet?


A. 37.49%
B. 12.51%
C. 87.49%
D. 89.44%

Answer 1

To find the probability that a randomly selected giraffe will be shorter than 18 feet, we can use the properties of the normal distribution.

We have:
- Mean (\(\mu\)) = 16.5 feet
- Standard deviation (\(\sigma\)) = 1.3 feet

We want to find the probability that a giraffe's height \(X\) is less than 18 feet, or \(P(X < 18)\).

First, we calculate the z-score for 18 feet using the formula:

\[
z = \frac{(X - \mu)}{\sigma}
\]

Substituting the values:

\[
z = \frac{(18 - 16.5)}{1.3} = \frac{1.5}{1.3} \approx 1.1538
\]

Next, we can look up the z-score in a standard normal distribution table or use a calculator to find the corresponding probability.

Using a standard normal distribution table or calculator, we find:

\[
P(Z < 1.1538) \approx 0.875 (or 87.5\%)
\]

This means that the probability that a randomly selected giraffe will be shorter than 18 feet is approximately 87.5%.

Thus, the answer is:

**C. 87.49%**.