# Normal distribution and standard deviation

#### godales77

##### New member
Can someone please help me with this problem. It's been killing me all day. I do not know how to find the first or third quartiles. Thanks. :/

The scores of students on an exam are normally distributed with a mean of 219 and a standard deviation of 69.

(a) What is the first quartile score for this exam?

(b) What is the third quartile score for this exam?

#### tutor_joel

##### Junior Member
So, the first quartile means that you want to know what the 25th percentile is for the given mean and the third quartile is the 75th percentile. Using your z table, look up the z value for the 25th percentile for part a. That is, the value 0.25 corresponds to what z value? It should be about -0.675. Do you know how to find this? Then just use this equation:

$$\displaystyle z=\frac{x - \mu}{\sigma}$$

You're solving for x here given mu and sigma and looking up z in the table.

$$\displaystyle x = z\sigma + \mu$$

In order to do part b, look up the z value for the 75th percentile and re-solve.

You should know that the first quartile should be a very low score and the 3rd quartile should be much larger. Just to get a sense if your answer is correct.

#### kpsingh

##### New member
The scores of students on an exam are normally distributed with a mean of 219 and a standard deviation of 69.

(a) What is the first quartile score for this exam?