[Statistic] NCE or just usual z-score?

[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?

Thanks for the answer. [PLAIN]"hyprotika.wordpress.com"[/URL]

 

[statdad]

If you want the percentage of women who lived to at least 50 you want to calculate

<br /> \Pr(X \ge 50)<br />

For the second question (I think this is what you are saying) if you can determine how many standard deviations 35 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.

 

[HallsofIvy]

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.

 

[master cherundo]

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

 

[master cherundo]

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