Z-scores Please help

On an exam with a population mean of 70 and standard deviation of 10, you have a score of 85.

a.) What is your z-score on this exam?

My answer: My z-score is 1.50

b.) If the instructor added 5 pts to every score, what would happen to your z-score?

Answer: ? I think that the z-score would stay the same.

C. If the instructor multiplied every score by 2, what would happen to the z-score?

Answer: This is the same as part b., right? So, if I got part b. correct, then the z-score would still stay the same here too?

I was able to get the answer to part a. (assuming it is right, anyhow). But, I am not sure about part b and c. I think that the z-score would stay the same. But, I am just not sure. Can someone please help me? Thank you for your time.

Z-scores measure how many standard deviations a value is from the mean (with its sign indicating direction).

A value with a z-score of 1.5 means it is one and a half standard deviations to the right of the mean.

For part b, I agree with your answer. What happens to the average when you add five to each quantity? It also increases by 5. What happens to the standard deviation? It remains the same (look at the formula, and think about it). Your new score then still lies the same number of standard deviations from the mean, so your z-score is unchanged.

Now for part c, investigate the same questions I gave you above. If you are unsure, pick some example data which agree with your given assumptions and try to draw a conclusion for it.