(sorry about creating a topic for this grammar point, but it doesn’t seem like one was made in the past)
if だいたい is considered a synonym, why wouldn’t I get a notice here? Why is it marked wrong if it has the same meaning?
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I believe だいたい would sound off here. Wrong register being too casual.
おおよそ is commonly used for delivery notices and the remainder of the sentence is in ‘business’ Japanese.
In addition to register, だいたい just isn’t used in these situations anyways. Its meanings range closer to “the majority of” or “usually”. If you were to use だいたい in this case you’d need to remove the 予定 part at the end and the sentence meaning would morph into “Ordered goods usually arrive in 2 weeks” with no specific mention of YOUR order.
おおよそ is much less picky and just tells you the next number is not exact. Think およそ三百メートル先左に曲がってください。