Probability help- simple question?

Question

Hi, I don't quite understand how to do this question-(the 2.5% is kind of confusing me)
Help please :)

...You decide that accepting women within the top 2.5% height bracket will be reasonable for your competition. The height of all women follows a normal distribution with a mean of 168 cm and a standard deviation of 9 cm.

Calculate the cut-off height (C) that ensures only women within the top 2.5% height bracket are allowed into the competition.

Answer 1

if it's a normal curve you have 68.3% of all values within +/- 1SD from the mean, 95.5% of all values within +/- 2SDs from the mean and 99.7% of all values within +/- 3SDs from the mean.

168+2*9=186cm (approximately)

OR

Z=(X-Average)/SD
look up the z-score for .95 (95%) (it's 95% not 97.5% because 100%-2.5% on the left - 2.5% on the right), it's gonna be around 1.7, and plug it into your formula
1.7=(X-168)/9
X=183.3cm

Answer 2

You need to find a Height such that 1-2.5% of heights are less than the one you find.

If you use a standard normal table P(Z < 1.96) = 0.975 = 97.5%

Then you use the Z = (C-mean)/std. deviation = 1.96 to find your cut off height. Solve for C since you know the mean and the standard deviation.

I got C = 185.64 cm

Answer 3

i haven't taken stat in 2 years and i don't have my notes with me. but i remember that in order to do this you just have to use one of the tables that you have and plug in the givens and you should be able to come up with what value within your distribution is at the top 2.5% mark, which would be the 97.5% mark.

i'm sorry i can't help more than that.