I buy and sell laser printer toners. The demand rate is $2000$ units per month, and its standard deviation

is $70$ units. $($Note: this is not a variance.$)$ Assume the demand follows a normal distribution. If I order it$,$

it takes $1\mathrm{.}5$ weeks on average for its delivery and its standard deviation is $0\mathrm{.}8$ week. $($One month is four

weeks.$)$ Now, I have $950$ units in stock. If I order $4000$ units now, what is the probability of having a

shortage cycle. Use the time unit of month. $(1$ month $=4$ weeks$)$

$($a$)(2$ points$)$ Get the distribution of the demand during lead time

$($b$)(3$ points$)$ Get the probability