In general, how do do you calculate the mean and standard deviation of a normal distribution given 2 values on the distribution with their respective probabilities?
Suppose that the ages of students in an intro to statistics class are normally distributed. We know that 5% of the students are older than 19.76 years. We also know that 10% of students are younger than 18.3 years.
What are the mean and standard deviation of the ages?
In my attempts to solve a similar problem I can't see how to calculate the mean or standard deviation without first knowing one of the two. I can find the z-score for 95% and 10%, and if I could somehow derive the values for 5% or 90% I could then average the 5% and 95% or 10% and 90% values to then find the mean, but I don't see a way to do so. Is it even possible to solve this problem or is there not enough information?