an association set a requirement that for female students must be at least 178cm tall. Heights of female students are normally distributed with a mean of 163cm and standard deviation of 8cm(based on survey data that has been conducted by HEMA). Suppose you are trying to decide whether to take new intake PALAPES-UTM and the actual number of female UTM students is around 5000 female students.

Due to the very low number of female students joining, the requirement of heights (for female students only) has been set lower than 178cm. What is the new height requirement if they target that top 17% of female students that will be joining? Provide detailed explanations and point to the statistical showing how/why the result comes to be