Find the $z$-score for which $70 \%$ of the distribution's area lies to its righ

Step 1 ：The z-score is a measure of how many standard deviations an element is from the mean. To find the z-score for which 70% of the distribution's area lies to its right, we need to find the z-score for which 30% of the distribution's area lies to its left, because the total area under the curve of a normal distribution is 1 or 100%.

Step 2 ：The z-score is calculated to be approximately -0.5244005127080407.

Step 3 ：Final Answer: The z-score for which 70% of the distribution's area lies to its right is approximately \(\boxed{-0.524}\).