Kroger is trying to determine how profitable its loyalty program is$.$ Two types of

customers are those who joined the loyalty program $($called $$loyals$)$ and those who did

not $($called $$non$-$loyals$).$ The cost of serving a loyal customer per week is $$10$ greater

than that of serving a non$-$loyal customer. Kroger collected a sample of $100$ customers

with $20$ loyals and $80$ non$-$loyals in it$.$ The average weekly spending of loyal and non$-$

loyal customers in the sample is $$110$ and $$80,$ respectively. The standard deviation of

spendings for loyal and non$-$loyal customers is $$20$ and $$10$ in the sample, respectively.

Given this information, is it profitable for Kroger to maintain a loyalty program