Suppose that the manager of a construction supply house determined from historical records that demand for sand averages $51$ tons. In addition, suppose the manager determined that demand during lead time could be described by a normal distribution that has a mean of $51$ and a standard deviation of $3$ tons. Answer the following questions assuming that the manager is willing to accept a stockout risk of no more than $2$ percent. Use Table B$\mathrm{.}2$

$($Round your answer to two decimal points.$)$

a$.$ What value of $z$ is appropriate?