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[Statistic] NCE or just usual z-score?

  • #1

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


[tex]X'=s'z+\overline{X}[/tex]
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 [tex]PR_{49.9}[/tex] or [tex]PR_{50}[/tex]? 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 [tex]PR_{50}[/tex] 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]
[h2]Homework Statement [/h2]



[h2]Homework Equations[/h2]



[h2]The Attempt at a Solution[/h2]
 
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Answers and Replies

  • #2
statdad
Homework Helper
1,495
35
If you want the percentage of women who lived to at least [tex] 50 [/tex] you want to calculate

[tex]
\Pr(X \ge 50)
[/tex]

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
HallsofIvy
Science Advisor
Homework Helper
41,833
955
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
So, it is 100%-PR(50), right?
Gosh, I do it with PR (49.9)
uuu.gif
 
  • #5
--EDITED--
Double post, sorry. "hyprotika.wordpress.com"[/URL]
 
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