Find the z-value that corresponds to each percentile for a standard normal distribution.
a) 25 th percentile
b) 50 th percentile
c) 80 th percentile
Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table.
a) The $z$-value that corresponds to the 25 th percentile is
b) The $z$-value that corresponds to the 50 th percentile is
c) The $z$-value that corresponds to the 80th percentile is

Step 1 ：To find the z-value that corresponds to each percentile for a standard normal distribution, we can use the Percent Point Function (PPF), which is the inverse of the Cumulative Distribution Function (CDF). The CDF gives the probability that a random variable is less than a certain value, and the PPF gives the value associated with a certain probability.

Step 2 ：Calculate the z-value for the 25th percentile: \(-0.6744897501960817\)

Step 3 ：Calculate the z-value for the 50th percentile: \(0.0\)

Step 4 ：Calculate the z-value for the 80th percentile: \(0.8416212335729143\)

Step 5 ：Final Answer: a) The z-value that corresponds to the 25 th percentile is \(\boxed{-0.674}\)

Step 6 ：Final Answer: b) The z-value that corresponds to the 50 th percentile is \(\boxed{0.0}\)

Step 7 ：Final Answer: c) The z-value that corresponds to the 80th percentile is \(\boxed{0.842}\)