Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area 0.3094 .

Step 1 ：The problem is asking for the z-score that corresponds to the cumulative area 0.3094 in a standard normal distribution. The cumulative area is the area under the curve to the left of the z-score. The z-score is a measure of how many standard deviations an element is from the mean. In a standard normal distribution, the mean is 0 and the standard deviation is 1.

Step 2 ：To find the z-score, we can use the inverse of the cumulative distribution function (CDF) for a standard normal distribution. The inverse CDF, also known as the quantile function or the percent-point function, returns the boundary value for the cumulative probability.

Step 3 ：Let's denote the cumulative area as \(p\), so \(p = 0.3094\).

Step 4 ：By using the percent-point function, we find that the z-score is approximately -0.4975517771755809.

Step 5 ：Rounding to two decimal places, the z-score that corresponds to the cumulative area 0.3094 in a standard normal distribution is approximately -0.50. This means that the value is approximately half a standard deviation below the mean.

Step 6 ：Final Answer: The z-score that corresponds to the cumulative area 0.3094 is approximately \(\boxed{-0.50}\).