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.

Quote:

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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?

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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:

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

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Yes, with a different z.