# [Statistic] NCE or just usual z-score?

• master cherundo
In summary, the average male life span was 37.6 years, with a standard deviation of 4.8 years. The average female life span was 41.2 years, with a standard deviation of 7.7 years. At what age is a female death at the same relative position in the distribution as a male death at age 35? If you want the percentage of women who lived to at least 50, you want to calculate \Pr(X \ge 50)
master cherundo

## Homework Statement

In an ancient culture, the average male life span was 37.6 years, with a standard deviation of 4.8 years The average female life span was 41.2 years, with a standard deviation of 7.7 years. use the properties of the normal distribution to find the following:
a. What percentage of men died before age 30?
b. What percentage of women lived to an age of at least 50?
c. At what age is a female death at the same relative position in the distribution as a male death at age 35?

## Homework Equations

$$X'=s'z+\overline{X}$$
using Standard Normal Distribution table to find percentile rank

## The Attempt at a Solution

Problem a a is clear for me, but I have a little doubt in b, because
I am confused about choosing between $$PR_{49.9}$$ or $$PR_{50}$$? Percentile rank is defined as at or below. So, if it is said at least, I have to choose lower number, but what is it? Is it 49.9; 49.99; 49.999; or... So that's why I think $$PR_{50}$$ is the best "hyprotika.wordpress.com"[/URL]

Problem c is just using z-score right? So I don't have to apply Normal Curve Equivalent here? Finding z-score for male rate, then using mean and standard deviaton for female rate, then that's the answer. Is it right?

Last edited by a moderator:
If you want the percentage of women who lived to at least $$50$$ you want to calculate

$$\Pr(X \ge 50)$$

For the second question (I think this is what you are saying) if you can determine how many standard deviations [tex] 35 [tex] is from the mean lifetime for men, you need to find the age for women that is the same number of standard deviations from their mean.

Since the normal distribution is a continuous distribution, not just integer valued, the probability a woman will live to be "exactly" 50 is 0 (the integral of the probility density "from 50 to 50" is 0). The probability a woman will live to be "greater than or equal to 50" and "greater than 50" are the same.

So, it is 100%-PR(50), right?
Gosh, I do it with PR (49.9)

--EDITED--
Double post, sorry. "hyprotika.wordpress.com"[/URL]

Last edited by a moderator:

## 1. What is the difference between NCE and z-score?

NCE (Normal Curve Equivalent) and z-score are both measures of relative standing in a normal distribution. NCE is a unitless score that ranges from 0-100, with 50 representing the mean and each standard deviation equal to 10 points. Z-score, on the other hand, is a standardized score that measures how many standard deviations a data point is from the mean. It has a mean of 0 and a standard deviation of 1.

## 2. When should I use NCE versus z-score?

NCE is often used in educational settings to measure student performance and growth over time. Z-score is commonly used in statistical analyses to compare data points from different distributions. Ultimately, the choice between NCE and z-score depends on the context and purpose of the analysis.

## 3. How do I calculate NCE and z-score?

To calculate NCE, you need to know the raw score, mean, and standard deviation of the data set. You can then use the formula (raw score - mean) / standard deviation x 10 + 50 to find the NCE. To calculate z-score, you need the raw score, mean, and standard deviation of the data set. The formula for z-score is (raw score - mean) / standard deviation.

## 4. What do NCE and z-score tell me about my data?

NCE and z-score both provide information about the relative position of a data point in a normal distribution. A higher NCE or positive z-score indicates that the data point is above the mean, while a lower NCE or negative z-score indicates that the data point is below the mean. NCE and z-score can also be used to compare data points from different distributions.

## 5. Can NCE and z-score be applied to non-normal distributions?

NCE is specifically designed for use with normal distributions and may not accurately represent data from non-normal distributions. Z-score, however, can be applied to any distribution as long as the data is approximately normally distributed. If the data is highly skewed or has extreme outliers, z-score may not be an appropriate measure of relative standing.

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