Question 11 of 18 This test: 18 point(s) possible This question: 1 point(s) possible Submit tes Use the standard normal table to find the $z$-score that corresponds to the given percentile. If the area is not in the table, use the entry closest to the area. If the area is hal between two entries, use the $z$-score halfway between the corresponding $z$-scores. If convenient, use technology to find the $z$-score. \[ \mathrm{P}_{20} \] Click to view page 1 of the table. Click to view page 2 of the table. The z-score that corresponds to $P_{20}$ is $\square$ (Round to two decimal places as needed) Next
Solution
Step 1 ：The question is asking for the z-score that corresponds to the 20th percentile in a standard normal distribution. 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. The 20th percentile means that 20% of the data is below this point.
Step 2 ：To find this, we can use the inverse of the cumulative distribution function (CDF), also known as the quantile function or the percent-point function.
Step 3 ：The z-score that corresponds to the 20th percentile is approximately -0.84. This means that 20% of the data in a standard normal distribution is below -0.84 standard deviations from the mean.
Step 4 ：Final Answer: The z-score that corresponds to \(P_{20}\) is \(\boxed{-0.84}\).
