$1.$ The demand for meat at a grocery store during any week is approximately normally distributed with a mean demand of $5000$ pounds and a standard deviation of $300$ pounds.$($a$)$ If the store has $5300$ pounds of meat, what is the probability that they will run out during a random week?$($b$)$ How much meat should the store have in stock per week so as to only run short $10\%$ of the time?