Answer
$P(x̄\lt67.3)$ has increased with the increase of the sample. It is beacuse as the sample size increases the standard deviation of the sample means decreases ($σ_{x̄}=\frac{σ}{\sqrt n}$). With a lower $σ_{x̄}$ we have a higher $z_0=\frac{x̄-μ_{x̄}}{σ_{x̄}}$, given that $x̄=67.3\gtμ_{x̄}=64$. And, as $z_0$ increases $P(x̄\lt67.3)=P(z\lt z_0)$ also increases.
$P(x̄\lt65.2)$ has decreased with the increase of the sample. It is beacuse as the sample size increases the standard deviation of the sample means decreases ($σ_{x̄}=\frac{σ}{\sqrt n}$). With a lower $σ_{x̄}$ we have a higher $z_0=\frac{x̄-μ_{x̄}}{σ_{x̄}}$, given that $x̄=65.2\gtμ_{x̄}=64$. And, as $z_0$ increases $P(x̄\gt65.2)=P(z\gt z_0)$ decreases.
Work Step by Step
Given above.
