Problem:

The average final grade is a 63 with a standard deviation of 10. Professor Moore wants to curve the final grades according to a normal distribution so that 10% of the grades are Fs, 20% are Ds, 40% are Cs, 20% are Bs and 10% are As.

Required:

Question: Determine the numerical grades that conform to the curve Professor Moore wants to establish.

Note: Please describe comprehensively and provide step by step solution.