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 \(\boxed{0.842}\)