Question

1. A lovely old lady, he told me, a bit muddled-headed, but at this age she was
entitled to be, wasn't she?
entitled to be - means
i) she was given a title because of her age.
ii) such behaviour was natural of an old lady.
iii) it was compulsory for her to behave so.
iv) she was free to do anything due to her old age.
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Answer 1

1. c) It was compulsory for her to behave so.

Entitled doesn't exactly mean compulsory or mandatory. but it is how a person is supposed or expected to behave.