$(10$ pts$)$ In $2019,$ Stony Brook Hospital admitted $12,775$ patients. In $2020,$ a $30\%$ increase in admissions is expected. The hospital has $380$ beds. Assume the hospital operates $365$ days a year and assume one patient per bed.

a$.$ If the average patient stays in the hospital for $7$ days, how many beds were empty, on average, in $2019?$

b$.$ If the average patient stays in the hospital for $7$ days, how many beds were empty, on average, in $2020?$