# Lower and upper quartiles for a normal distribution?

• Mar 9th 2010, 04:58 AM
mrtoilet
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

• Mar 9th 2010, 05:10 AM
mr fantastic
Quote:

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

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 ....
• Mar 9th 2010, 06:54 AM
mrtoilet

Lower quartile - 28.25
Upper quartile - 37.4
• Mar 9th 2010, 05:37 PM
mr fantastic
Quote:

Originally Posted by mrtoilet

Lower quartile - 28.25
Upper quartile - 37.4

One of them is correct. (By the way, by symmetry both cannot possibly be correct ....)
• Mar 9th 2010, 06:42 PM
mrtoilet
Lower quartile - 30.65
Upper quartile - 37.35?
• Mar 9th 2010, 10:34 PM
mr fantastic
Quote:

Originally Posted by mrtoilet
Lower quartile - 30.65
Upper quartile - 37.35?

Close enough.