We've got normal distribution $N(\mu, \sigma)$ and sampled results: $[-5, 5, -10, 15, 25, 10, 0, 20, 10, 30]$. How to calculate probability of population mean will be greater than zero?
$\hat{\mu} = 10$
$\hat{\sigma} \approx 12.25$
$n = 10$
$P(\mu > 0) = ?$