A company uses the analysis of receivables method by aging its accounts receivable. Based on the following information, answer questions a$)$ and b$)$ below.

$\backslash$table$[[$Age Interval,Balance,Percent Uncollectible$],[$Not past due,$$865,000,18],[1-30$ days past due,$110,000,28],[31-90$ days past due,$65,000,158],[91-180$ days past due,$42,000,608],[$over $180$ days past due,$15,000,908]]$

$($a$)$ Calculate an estimate of what the allowance for doubtful accounts balance should be at fiscal year end $(3$ points$).$

$($b$)$ Assuming the allowance for doubtful accounts has a credit balance of $$6,500$ prior to adjustment, determine the appropriate adjusting entry necessary to adjust uncollectibles at fiscal year end $(3$ points$)$