$.$ According to last year$$s records, the number of mothers who delivered their

babies in a local hospital was $3,460,$ with a relatively steady birth rate over the

year. From historical data, it is known that most women stay in the maternity

ward for $2$ days before going home with their child $($or children in case of

twins$).$ However, sporadically, there are complications with the birth that

require longer stays. Over the last months, $92\%$ of the births have resulted in

$2-$day stays; for the remaining $8\%$ of the cases, the average length of time the

mothers had to stay in the maternity ward was $6$ days.

a$.$ Estimate the average length of time the mothers spend in the maternity

ward. $(20\%)$

b$.$ Provide an estimation about the minimum number of beds the

maternity ward should have. $(40\%)$

c$.$ Assuming that the maternity ward has in fact the number of beds you

have indicated in question $($b$)$ above, how many doctors should be

available between $9$:$00$ am and $11$:$00$ am every day, if the daily

examination of each mother would on average last $15$ minutes and all

examinations should take place during those $2$ hours $($each

examination to be carried out by only one doctor$)?$