The Two Control Limit for 3 Sigma $\bar { x }$

The two control limit for 3 sigma $\bar { x }$ chart have been calculated. If the variable of interest is normally distributed, and 3 is replaced by 3.09 in the control limits formulas, then probability of Type I error $( \alpha )$ __________, but for any fixed n and $\sigma$ , probability of Type II error $( \beta )$ will __________.