According to Baymard, 35% of ecommerce sites still display delivery information in this form:

You’ll get your order in three days

Or the even worse:

You’ll get your order in three to five business days.

What should you do instead?

Display the expected delivery date. Something like this: You will receive your order on May 27th.

If an exact delivery date is indeterminable, then a range of dates is acceptable though an exact date is always preferable.

Why is displaying the number of days instead of the date wrong?

It’s wrong because you are giving your customers too much work. There are too many elements to factor into delivery calculations. Let’s look at some of them:

Lead time: This is the time it takes you to prepare an order for shipment. Lead time can be quite negligible if all you’re doing is sticking a label on a shoebox containing pre-made shoes for shipment or quite a lot if you have to make a brand new pair of custom shoes by hand. A customer has no way of knowing your lead time.
Processing cut-off times: Let’s say you offer next-day delivery and don’t process orders after 3pm or on weekends. What happens when a customer places an order at 3.30pm on a Friday? Unless you make your processing cut-off times clear, you’re going to have one very pissed customer come Monday as the order was expected on Saturday.
Skipped dispatch days: Customers won’t to assume that their orders are dispatched as soon as possible, preferably within hours or even minutes of being placed. Yet this is rarely the case. There are days when you might not dispatch orders, maybe on weekends or holidays. If you don’t ship out products in large quantities, your shipping provider may not pick up packages from your warehouse on a daily basis.
Order volume requirements: If you are making deliveries yourself rather than relying on a shipping provider, you might need a certain volume of orders so as to make a delivery run economically viable. A customer doesn’t have access to this information.
Customs: When shipping internationally, it might take some time for your goods to clear customs especially if they aren’t exempted by a free trade agreement. Depending on the efficiency of the government in question, this process can take a few hours, days, or even weeks.

Why do customers need exact delivery dates?

Exact delivery dates might not super important for stuff like novelty cups but there are multiple instances when an exact delivery date can make or break a sale:

Security for high ticket items: If someone is buying something like a thousand-dollar computer or an expensive piece of jewelry, they’ll probably want to be home to receive it when it comes.
Special occasions: Someone ordering a birthday cake or chocolates for Valentines day wants their order delivered on that exact day, not the day after.
Customer convenience: Someone going on a holiday might want their order delivered before they leave or after returning from their holiday. Lack of an exact delivery date will make them wonder whether their purchase will be lying on the porch for a month, completely exposed to the elements and that’s assuming no one bothers to steal it.