# Zack takes the SAT and his best friend Nick takes the ACT. Zack’s SAT math score is 680, and Nick’s ACT math score is 27. SAT math scores in the county are normally distributed, with a mean of 500 and a standard deviation of 100. ACT math scores in the county are also normally distributed, with a mean of 18 and a standard deviation of 6. Assuming that both tests measure the same kind of ability, who has scored better?

##### 1 Answer

Zack has scored better than Nick.

To compare the two scores, you should convert their scores to a

To convert a random variable (the person's score) into a

So, first plug in the corresponding numbers for Zack:

Then, plug in the corresponding numbers for Nick:

As you can see,

Source: Wikipedia