Mathematics Homework Help

Foot lengths and foot widths of adult European women can be well modelled with a bivariate normal distribution. The pair of random variables (X,Y) measures (in mm) the foot (length,width) of a randomly chosen European woman. Assume that

and that foot widths and foot lengths of different random women are independent.

1. A European woman has feet that belong to the 20% longest feet. What is the minimal length of her feet?
2. What is the proportion of all European women with a foot length that is 150 mm larger than the foot width?
3. Of how many random European women do you need to measure the foot width in order to find, with at least 90% probability, at least 60 women with feet that are wider than 100 mm

final answer is not sufficient, calculation must include description of random variables, mentioning the applied mathematical property and why it holds, answer should be atleast 4 significant figures.