What are the two formulae to convert between the two?
For example, I have a z critical value of 3.00. With what formula can you convert this to 0.9973?
And, for example, you have a confidence level value of 0.9973. How do you convert it to 3.00?
0.9973 is (approximately) the area under a normal curve between a z-score of -3 and a z-score of 3. This isn't what is normally called a confidence level. The formulas you are being given are the formulas to find the cumulative probability under the curve up to your z-score. This is more like what would be called a critical value.
You probably should get a basic statistics textbook and study the chapter on z-scores and figuring areas under the normal distribution. Your answer will be explained there
– Steve Scher Jan 28 '20 at 21:42