Questions: 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 halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. P8 The z-score that corresponds to P8 is (Round to two decimal places as needed.)

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 halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score.
P8

The z-score that corresponds to P8 is (Round to two decimal places as needed.)

Transcript text: 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 halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the $z$-score. $\mathrm{P}_{8}$ The z -score that corresponds to $\mathrm{P}_{8}$ is (Round to two decimal places as needed.)

Solution

Solution Steps

Step 1: Understanding the Problem

We need to find the z-score that corresponds to the 8th percentile, denoted as $ P_8 $. This means we are looking for a z-score such that the area to the left of it under the standard normal curve is 0.08.

Step 2: Using the Percentile Function

To find the z-score corresponding to the 8th percentile, we use the percent point function (PPF) of the standard normal distribution. The PPF gives us the z-score for a given cumulative probability.

Step 3: Calculation

Using the PPF for the standard normal distribution, we find:

\[ z = PPF(0.08) \approx -1.410 \]

Step 4: Rounding the Result

We round the z-score to two decimal places:

\[ z \approx -1.41 \]