I am working on a self-study question where
A study indicates that the typical American woman spends USD 340 per year for personal care products. The distribution of the amount follows a right-skewed distribution with a standard deviation of USD 80 per year. If a random sample of 100 women is selected, what is the probability that the sample mean of this sample will be between USD320 and USD350?
I made two attempts to answer the question: one using normal distribution and another using CLT. However, neither approach has helped me achieve the goal answer of 0.8882.
My Normal Distribution Approach
My CLT Approach
Appreciate some guidance and advice please