Z score

[Tahnan Tasnim]

I'm having some trouble with my homework. The question is --

In a distribution with mean of 71 and a standard deviation of 18, there exists a score of 85. What is the equivalent score in a distribution with a mean of 50 and a standard deviation of 10?

My question is, are the z scores here gonna be the same? If so, then the z score is 0.78 and the equivalent score is 57.8
Please correct me if I'm wrong.

 

[Dr.Peterson]

In a distribution with mean of 71 and a standard deviation of 18, there exists a score of 85. What is the equivalent score in a distribution with a mean of 50 and a standard deviation of 10?

My question is, are the z scores here gonna be the same? If so, then the z score is 0.78 and the equivalent score is 57.8

That's right, if you were told to round to the nearest tenth.

I'd feel better about the problem if it explicitly told you both distributions were the same type, e.g. normal.

 

[Tahnan Tasnim]

Could you please explain what you meant by if I were told to round to the nearest tenth?
Thanks

 

[Dr.Peterson]

Could you please explain what you meant by if I were told to round to the nearest tenth?
Thanks

The z-score is actually (85-71)/18 = 0.7777777..., so the equivalent score in the second distribution is 50 + 10*0.7777777... = 57.777777... .

So if you were told to round your answer to the nearest hundredth, say, then the answer would be 57.78. And so on.

If the instructions said to round to the nearest tenth, then you were right with 57.8.

Sometimes students wonder why a computer rejected their answer, and it turns out to be something like that, so I thought I'd mention that in case it was a useful reminder. Apparently it wasn't.