Yes, Hair dryers are available in all staterooms.
The amenities the ship's stateroom is just as in any hotel. Mini-fridge, phone, TV, coffee maker (not in inside & ocean view staterooms), ice bucket, beach towels, mini-safe, hair dryer, liquid soap and shampoo.
You can use internet on your phone or ipad but if you plan to use the ship's wifi then you have to purchase the internet minutes.
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Phone-you can connect to your carrier while in port. -if it's an Alaska port (don't know what cruiise you are going on).You can also connect the Internet through wi fi while on ship for a price. Since there are no cell towers at sea,your phone won't work as a phone while sailing.
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