What I have done: read statistics text (Statistics - informed decisions using data) and the posted online learning by the instructor, multiple times. My calculations:

Left Tail Test: 55 - 2.575 (20/ sq of 64: 8) = 48.5625

P (Type II error): (50 - 48.5625) / (20/ sq of 64: 8) = 0.575

This should equal .7157 probability of a Type II error

I know this is not the correct answer. I just can't figure out what I am doing wrong. any articles or references or advise on here would be much appreciated.