I had a disagreement with my professor about this specific problem recently and so I though it would be good to get some other input on the matter. Here's the question:
22% of a population of fish are more than 45 cm in length and 14 % are more than 55 cm in length. What is the mean length and standard deviation of the lengths of the fish?
We were given a z-score lookup table to solve this problem with the following values: -0.77 -> 0.2206 and 0.78 -> 0.2177
I used the z-score value of -0.77, converted to 0.77, because the percentage was closer to the 22% from the question. However my professor believed the correct value should be 0.78. I believe his reasoning was that you needed to have a z-score value that fit within the 22% of data because the question said more than 22%.
Any discussion/help would be appreciated, thanks!