A word has been given in the question and used in the sentences below. Identify the statements where the word has been used in a contextually and grammatically correct manner.

GAIT

(I) The security guard stood at the school gait to check the identity cards of visitors.

(II) The doctor assessed the patient’s gait to check for any signs of mobility issues.

(III) The entrance gait to the park was decorated with colorful lights for the festival.

To determine the correct usage of the word GAIT, let us first look at its definition and distinguish it from its homophone gate.

Gait: A noun that refers to a person's manner of walking or moving on foot (e.g., "a steady gait").
Gate: A noun that refers to a hinged barrier used to close an opening in a wall, fence, or hedge (e.g., "the school gate").

Now, let us analyze each statement based on these definitions:

(I) The security guard stood at the school gait to check the identity cards of visitors.
In this context, the sentence refers to a physical barrier or entrance of the school. Therefore, the correct word should be gate, not "gait". This statement is contextually incorrect.

(II) The doctor assessed the patient’s gait to check for any signs of mobility issues.
Here, the sentence refers to checking the patient's manner of walking to identify mobility problems. This is the precise and correct definition of gait. This statement is contextually and grammatically correct.

(III) The entrance gait to the park was decorated with colorful lights for the festival.
Similar to statement (I), this sentence refers to the physical entrance barrier of the park. The correct word should be gate, not "gait". This statement is contextually incorrect.

Therefore, the word GAIT is used correctly in statement (II) only.