Math Problem Solver

https://math-gpt.org/?problem_text=Triangle%20R%20has%20been%20rotated%20%5C(%20%5Csquare%20%5C)%20clockwise%2Fanticlockwise%20by%20%5C(%20%5Csquare%20%5C)%20%5C(%20%5D%5E%7B%5Ccirc%7D%20%5C)%20about%20the%20point%20%5C(%20(%5Csquare%2C%20%5Csquare)%20%5C)%20to%20give%20triangle%20%5C(%20S%20%5C).Solve%20the%20above%20math%20problem.&answer_text=MathGPT%20Unlimited%20Messsage%20a.%20The%20population%20mean%20(%CE%BC_x%CC%84)%20is%20simply%20the%20same%20as%20the%20average%20salary%20for%20the%20profession%2C%20which%20is%20%2474%2C000.%0A%0Ab.%20The%20standard%20deviation%20of%20the%20sample%20mean%20(%CF%83_x%CC%84)%20is%20given%20by%20%CF%83%2F%E2%88%9An%2C%20where%20%CF%83%20is%20the%20population%20standard%20deviation%20and%20n%20is%20the%20sample%20size.%20Plugging%20in%20the%20given%20values%2C%20we%20get%3A%0A%CF%83_x%CC%84%20%3D%2037000%2F%E2%88%9A79%20%E2%89%88%204162.83%0A%0Ac.%20The%20shape%20of%20the%20sampling%20distribution%20of%20x%CC%84%20is%20that%20of%20a%20normal%20distribution%2C%20as%20given%20by%20the%20Central%20Limit%20Theorem%20for%20large%20sample%20sizes.%20So%2C%20the%20correct%20answer%20is%20B.%20The%20shape%20is%20that%20of%20a%20normal%20distribution.