Answered

IDNLearn.com provides a collaborative environment for finding and sharing knowledge. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.

Evaluate the z-score that corresponds to the 65th percentile in the standard normal distribution.

Sagot :

GinnyAnsweridn
Sure, let's walk through the process of finding the z-score that corresponds to the 65th percentile in a standard normal distribution.

1. Understanding Percentiles in a Standard Normal Distribution:
- A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
- The percentile represents the point below which a given percentage of observations fall. So, a 65th percentile means that 65% of the data falls below this point.

2. Using Standard Normal Distribution Tables (z-tables):
- To find the z-score for a given percentile, we can refer to standard normal distribution tables which provide the area (or cumulative probability) to the left of a given z-score.
- The 65th percentile corresponds to an area of 0.65 to the left of the desired z-score.

3. Locating the 65th Percentile in the Z-Table:
- If we look up the cumulative probability of 0.65 in the z-table or use statistical software or calculators designed for this purpose, we would find the z-score that matches this probability.

From the above steps, the z-score that corresponds to the 65th percentile in a standard normal distribution is approximately:
[tex]\[ \boxed{0.3853} \][/tex]

So, the z-score corresponding to the 65th percentile in a standard normal distribution is approximately 0.3853.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.