Type II error hypothesis question

[theBEAST]

Homework Statement

Here is the question (I am only confused about part b):

Here is the solution given by my professor:

The Attempt at a Solution

However, I do not agree with part b and honestly have no clue where they got that formula from. I used the method taught in my class along with a bit of intuition and came up with a beta value of 0.4825. Does anyone agree with me work or is the solution from the professor actually correct?

 

[theBEAST]

Anyone got an idea? :O