Answer
There is not sufficient evidence to not support that the earthquakes don't have a mean depth of 10 kms.
Work Step by Step
$H_{0}:\mu=10$. $H_{a}:\mu \ne10.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{9.81-10}{5.01/\sqrt{50}}=-0.27.$ The P-value is the probability of z being less than -0.27 or bigger than 0.27 which is the sum of the probability of the z-score being less than -0.27 plus 1 minus the probability of the z-score being less than 0.27, hence:P=0.3936+1-0.7064=0.5028. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is more than $\alpha=0.01$, because it is 0.5028, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to not support that the earthquakes don't have a mean depth of 10 kms.
