Thread: Lower and upper quartiles for a normal distribution?

X is a random variable that follows a normal distribution with a mean of 34 and a standard deviation of 5.
a) What proportion of X’s values lie between 30 and 40?
b) Find the lower and upper quartiles of X’s distribution.


Can someone check my answer for a) (please tell me where I went wrong, if it is incorrect):
= P(30-34/5) < Z < P(40-34/5)
= P(-.8) < Z < P(1.2)
= P(Z < 1.2) - P(Z < -.8)
= .8643 - .2119
= .6524

And for b), I have no idea what to do, please help!

Originally Posted by mrtoilet

X is a random variable that follows a normal distribution with a mean of 34 and a standard deviation of 5.
a) What proportion of X’s values lie between 30 and 40?
b) Find the lower and upper quartiles of X’s distribution.


Can someone check my answer for a) (please tell me where I went wrong, if it is incorrect):
= P(30-34/5) < Z < P(40-34/5)
= P(-.8) < Z < P(1.2)
= P(Z < 1.2) - P(Z < -.8)
= .8643 - .2119
= .6524

And for b), I have no idea what to do, please help!

a) I get 0.6731 (but you're probably using tables, which leads to inaccuracies).

b) Do you know the definition of lower and upper quartile? Then the problem is simply an inverse normal problem ....

Can someone check my answers:

Lower quartile - 28.25
Upper quartile - 37.4

Originally Posted by mrtoilet

Can someone check my answers:

Lower quartile - 28.25
Upper quartile - 37.4

One of them is correct. (By the way, by symmetry both cannot possibly be correct ....)

Lower quartile - 30.65
Upper quartile - 37.35?

Originally Posted by mrtoilet

Lower quartile - 30.65
Upper quartile - 37.35?

Close enough.