The scores on a mathematics exam have a mean of 65 and a standard deviation of 8 . Find the $x$-value that corresponds to the $z$-score 3.532 .
61.5
100.3
29.7
93.3

Step 1 ：The z-score is a measure of how many standard deviations an element is from the mean. In this case, we are given the z-score, the mean, and the standard deviation, and we are asked to find the corresponding x-value.

Step 2 ：We can use the formula for the z-score to solve for x: \(z = (x - μ) / σ\), where z is the z-score, x is the value we're looking for, μ is the mean, and σ is the standard deviation.

Step 3 ：Rearranging the formula to solve for x gives us: \(x = zσ + μ\).

Step 4 ：We can plug in the given values into this formula to find the x-value: \(z = 3.532\), mean = 65, std_dev = 8.

Step 5 ：Calculating gives us: \(x = 3.532 * 8 + 65 = 93.256\).

Step 6 ：Final Answer: The \(x\)-value that corresponds to the \(z\)-score 3.532 is \(\boxed{93.256}\).