To find the mean [tex]\(\mu_p\)[/tex] for the given scenario, we use the fact that [tex]\(\mu_p\)[/tex] represents the expected proportion of teenagers who own smartphones in the sample.
In a binomial distribution, the mean of the sample proportion [tex]\(\mu_p\)[/tex] is given by:
[tex]\[
\mu_p = p
\][/tex]
where [tex]\(p\)[/tex] is the probability of success, which in this case is the proportion of teenagers who own smartphones.
Given that the probability [tex]\(p\)[/tex] is [tex]\(80 \%\)[/tex] or [tex]\(0.80\)[/tex], the mean [tex]\(\mu_p\)[/tex] can be directly determined as follows:
[tex]\[
\mu_p = p = 0.80
\][/tex]
Therefore,
[tex]\[
\mu_p = 0.8000
\][/tex]
Thus, the mean [tex]\(\mu_p\)[/tex] is [tex]\(\boxed{0.8000}\)[/tex].
