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I have a 6 sided die with the numbers 1, 2, 3, 3, 4, 5 on...

I have a 6 sided die with the numbers 1, 2, 3, 3, 4, 5 on it. I also have a hat filled with numbers. When I pick a number out of the hat, I get a number between 1 and 10. The hat number has a mean of 2 and a standard deviation of 2.5. I make a new random variable by combining these two previous random variables. The new random variable is made by taking the number I get from the hat and multiplying it by 7 and then adding 3. Then I add the number I rolled on the die. For example if I pick a 6 out of the hat and roll a 2 on the die my new random variable is 7(6) + 3 + 2 = 47.

What is the mean and standard deviation of the new random variables?

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