Answer questions $9,10$ and $11$ based on the case and data given in the following: An industrial engineer applies work sampling to an quality control operator. She makes $600$ observations throughout a work week. In $480$ observations the operator performs quality control of a product, and he was idle in remaining $120$ observations. During sampling week, operator's total work duration is $40$ hours, and he controlled totally $1600$ parts. Mean Westinghouse rating is $1\mathrm{.}25$ for the operator, and $30\%$ allowances are applied to this task. $($Round up your result if necessary$)$

$9.(5$ points$).$ Based on these data, what is the mean cycle time for controlling one product $($Calculate in seconds$)?$

a$.)48$ seconds

b$.)32$ seconds

c$.)15$ seconds

d$.)144$ seconds

e$)72$ seconds