Scarlett next researches the most time$-$intensive stationary part required to assemble the MX$332.$ She types a command into the computer to generate a list of parts required to assemble the MX$332.$ She then types a command to list the average delivery time for each part. She learns that part $10003487$ typically requires the longest time to complete, and that this part is only used for the MX$332.$ She investigates the pattern for the part further and learns that over the past year, part $10003487$ has taken an average of three fourths $(3/4)$ of month or $22\mathrm{.}5$ days $($assume $1$ month $=30$ days$)$ to complete once an order is placed. She also learns that the factory can produce the part almost immediately if all the necessary raw materials for the production process are on hand. So the completion time actually depends on how long it takes to obtain these raw materials from the supplier. On those unusual occasions when all the raw materials already are available in inventory, the completion time for the part is essentially zero. But sometimes the completion time can be as high as one and a half months. For the lack of a better estimate Scarlett assumes that this completion time also follows a normal distribution.

$($b$)$ What is an estimate of the mean and variance of the delivery time for part $10003487?$