Please refer the image below:

$($a$)$ The local supermarket buys lettuce each day to ensure really fresh produce. Each morning, any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who nee it to feed their animals. This week, the supermarket can buy fresh lettuce for $$4\mathrm{.}00$a box. The lettuce is sold $$10\mathrm{.}00$ a box and the dealer that sells old lettuce is willing to pay $$1\mathrm{.}50$ a box. Past history says that tomorrow's demand for lettuce averages $250$ boxes with a standard deviation of $34$ boxes. Demand follows an approx. normal distribution.

$($i$)$ How many boxes of lettuce should the supermarket purchase tomorrow?

$($ii$)$ Based on part $($i$),$ what is the probability that the supermarket will run out of stock? $(0\mathrm{.}54)=0\mathrm{.}7054$;$,(0\mathrm{.}55)=0\mathrm{.}7088$;$,L(0\mathrm{.}54)=0\mathrm{.}1857$;$,L(0\mathrm{.}55)=0\mathrm{.}1828$