Find the $z$-score for which $70 \%$ of the distribution's area lies to its right.
$-1.52$
$-0.52$
$-0.84$
$-2.48$
Answer
Final Answer: The z-score for which 70% of the distribution's area lies to its right is approximately \(\boxed{-0.52}\).
Step 1 ：The z-score is a measure of how many standard deviations an element is from the mean. In this case, we are asked to find the z-score for which 70% of the distribution's area lies to its right. This means that 30% of the distribution's area lies to its left.
Step 2 ：We can use the percentile point function to find the z-score corresponding to the 30th percentile.
Step 3 ：Let's denote the percentile as 0.3.
Step 4 ：After calculation, we find that the z-score is approximately -0.5244005127080409.
Step 5 ：Final Answer: The z-score for which 70% of the distribution's area lies to its right is approximately \(\boxed{-0.52}\).
