Answer:
mean = 157
standard deviation = 0.77
From the given, we know that:
[tex]\begin{gathered} \mu=157 \\ \sigma=3 \end{gathered}[/tex]Now, since we are to select 15 bottles as samples, we now have n=15. We would then need to solve for standard deviation with the following formula:
[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]Substitute the standard deviation and n:
[tex]\begin{gathered} \sigma_{x}=\frac{\sigma}{n} \\ \sigma_x=\frac{3}{\sqrt{15}} \\ \sigma_x=0.77 \end{gathered}[/tex]The mean would stay the same, therefore:
mean = 157
standard deviation = 0.77
