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

1. Oct 6, 2008

### master cherundo

1. The problem statement, all variables and given/known data
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?

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

3. 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?

[b]1. The problem statement, all variables and given/known data[/b]

[b]2. Relevant equations[/b]

[b]3. The attempt at a solution[/b]

Last edited by a moderator: Apr 23, 2017
2. Oct 6, 2008

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.

3. Oct 6, 2008

### HallsofIvy

Staff Emeritus
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.

4. Oct 8, 2008

### master cherundo

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

5. Oct 8, 2008

### master cherundo

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

Last edited by a moderator: Apr 23, 2017