Could you please solve the problem below? I need detailed mathematical process steps and explanation. A study on the length of time a person brushes their teeth is conducted on a large population of adults. The mean brushing time is $\backslash$mu and the standard deviation is $\backslash$sigma$.$ A simple random sample of $270$ adults is considered.

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$($a$)$ The mean of the sampling distribution is $?$

the mean of the population.

$($b$)$ The standard deviation of the sampling distribution is $?$

the standard deviation of the population.