Smartphones: A poll agency reports that [tex]$80 \%$[/tex] of teenagers aged [tex]$12-17$[/tex] own smartphones. A random sample of 250 teenagers is drawn. Round your answers to four decimal places as needed.

Part: [tex]$0 / 6$[/tex]

Part 1 of 6

(a) Find the mean [tex]$\mu_p$[/tex].

The mean [tex]$\mu_p$[/tex] is [tex]$\square$[/tex].



Answer :

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].