Question

The 1-Mile Run is a common test for assessing physical fitness. Among college males the 1-Mile Run time is normally distributed with a mean of 436 seconds and standard deviation of 70 seconds.
What's the third quartile of this population?

Answer 1

Third quartile is at p=.75
Use normal distribution table or calculator to find the x associated with the z-score of N(436,70)

Answer 2

So p=.75 is that the same as z=.75

Answer 3

No, the z will depend on the mean and standard deviation.

Answer 4

Or rather, the z depends on p, then the x you need to find will depend on the mean and standard deviation.

Answer 5

You'll need an inverse normal function on a calculator or do a reverse lookup in a normal distribution table to find z, then use the z formula to solve for x.
\[z=\frac{x-µ}{σ}\]

Answer 6

I been using that formula but idk what to set z as once I have z I can solve for x and that would be my answer. Can u tell me what my z should be

Answer 7

Do you have a z-table handy? You can find tables of z-scores online as well as distribution calculators. You should get used to using those.

Answer 8

I do so do I look up .75 on the table and use .773 from the table and set it to z in the formula .773= (X - 436) / 70

Answer 9

Are you sure about that .773? I'm getting .6745

Answer 10

That's my problem I'm thinking I'm using the wrong table

Answer 11

Could be..
Try this one
http://www.math.unb.ca/~knight/utility/NormTble.htm

Answer 12

Yeah I'm using that .75 I'm getting .773

Answer 13

Oh, I see what's happening. You're reading down the z column looking for p, but the p is in the body of the table, then you have to read across from there to the margin to find z.

Answer 14

That's why it's called a reverse-lookup, you do it backwards from how you would if you had z and were trying to find p.

Answer 15

p(z = 0.75) = 0.7734, but you want p(z = ?) ≈ .7500
It's likely you won't find .75 exactly, so find the two numbers that are closest and estimate.

Answer 16

Oh thanks I see now