A normal distribution has mean 65.1 and standard deviation 4.93. Find the data value corresponding to the following value of $z$.
$$z=-0.36$$
The data value corresponding to $z=-0.36$ is (Round to the nearest tenth as needed.)

Step 1 ：We are given a normal distribution with mean $\mu =65.1$ and standard deviation $\sigma =4.93$. We are asked to find the data value corresponding to the z-score $z=-0.36$.

Step 2 ：The z-score is a measure of how many standard deviations an element is from the mean. The formula for the z-score is $z=\frac{x-\mu }{\sigma }$, where $x$ is the data value we are trying to find.

Step 3 ：We can rearrange this formula to solve for $x$: $x=z\cdot \sigma +\mu$.

Step 4 ：Substituting the given values into this formula, we get $x=-0.36\cdot 4.93+65.1$.

Step 5 ：Calculating the above expression, we get $x=63.325199999999995$.

Step 6 ：Rounding to the nearest tenth as needed, we get $x=63.3$.

Step 7 ：Final Answer: The data value corresponding to $z=-0.36$ is $\boxed{{\displaystyle 63.3}}$.