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I attempted the problem and came up with this:

u=55 and sd = 8 (Square root of 64)

[tex]\mu=55 \sigma=\sqrt{64}=8[/tex]

[tex]P(53< \bar{X} < 57) = P(\frac{53-55}{\frac{8}{\sqrt{256}}}<Z<\frac{57-55}{\frac{8}{\sqrt{256}}})=P(-4<Z<4)[/tex]

What am I doing wrong?