A client has asked you to design a lifting beam to lift and handle nuclear waste containers. Based on calculations you performed using the geometry of the containers themselves and their contents, you expected them to weigh $100$ kg$.$ The client weighed several sample containers and found that they weigh $99$ kg on average with a standard deviation of $13\mathrm{.}2$ kg$.$

Past statistical studies of steel beams available in the literature found that their geometric, professional, and material bias were $0\mathrm{.}99,1\mathrm{.}0,$ and $1\mathrm{.}07,$ respectively. The coefficients of variation were $0\mathrm{.}021,0\mathrm{.}05,$ and $0\mathrm{.}06,$ respectively.

Given the consequences of mishandling nuclear waste, you want to provide a low risk of failure, so calculate the factor of safety you should use to provide a reliability index of $10.$

Provide your answer to two $(2)$ decimal places.