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?(1 point)
Responses

37.49%
37.49%

87.49%
87.49%

12.51%
12.51%

89.44%

Answer 1

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

Given:
- Mean (μ) = 16.5 feet
- Standard deviation (σ) = 1.3 feet

First, we need to find the z-score for 18 feet:

\[
z = \frac{(X - μ)}{σ}
\]

Where:
- \(X\) = 18 feet
- \(μ\) = 16.5 feet
- \(σ\) = 1.3 feet

Substituting the values:

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

Next, we can use a z-table (or a standard normal distribution calculator) to find the probability corresponding to a z-score of approximately 1.15.

Looking up this z-score, we find that the cumulative probability for \(z = 1.15\) is approximately 0.8750 (or 87.50%).

Therefore, the probability that a randomly selected giraffe will be shorter than 18 feet is approximately **87.49%**.

So the correct response is:

**87.49%**