# Determine Score

• Sep 9th 2005, 08:52 PM
sarugaki
Determine Score
I'm doing an on-line stats class and need some clarification.

info as follows:

mean=174.5centimeters
standard deviation = 6.9centimeters

What is the probability that 1 randomly selected person's height is greater than
185centimeters?

I calculated it as:

z= 185-174.5 / 6.9

z= 1.5

Using Z-Score table I determined 1.5 = .9332 resulting in 1-.9332 = .0668

So there is a 6.68% probability of 1 person's height being > 185centimeters.

So far so good; however the follow on question ask to find two heights that seperate the top 25% and the bottom 20% of the population.

Question 1: Using x = u + (z * standard deviation) for the top 25%, do I look up .25 on the table (-1.96) and solve for the top 25% height, because I get a number that is < the mean height of 174.5?

x=174.5 + (-1.96 * 6.9) = 160.976

Question 2: Is the process the same for the bottom 20%?

Appreciate any suggestions.
• Oct 6th 2005, 04:42 PM
hpe
Quote:

Originally Posted by sarugaki
So far so good; however the follow on question ask to find two heights that seperate the top 25% and the bottom 20% of the population.

Question 1: Using x = u + (z * standard deviation) for the top 25%, do I look up .25 on the table (-1.96) and solve for the top 25% height, because I get a number that is < the mean height of 174.5?

You looked up 0.025 on your table. You need to look up 0.75 (!), because that would be the probability to the leftt of the desired height; 0.25 is to the right Then the rest bis OK.

x=174.5 + (-1.96 * 6.9) = 160.976
Quote:

Question 2: Is the process the same for the bottom 20%?
Yes, with a different z.