What do you mean by true mean? I guess you have already specified true population mean as 36.0 lbs in first line. In your calculation, you have used this value as alternative hypothesis. (u1 = 38.25)f the true mean μ1=38.25 lb., compute the probability of a type II error (β) assuming that the type I error has not changed.

I think value in the denominator should be 2.=p(34.71- 38.25/0.5<xbar- /σ/sqrt(n)< 37.29- 38.25/0.5|1= 38.25)