In: Statistics and Probability
Bird’s data analyst wants to model the sample mean and sample
variance of net revenue of scooters. They plan to take a random
sample of 25 of its scooters in Austin. They will record weekly net
revenue brought in by each scooter. They decide it is reasonable to
assume that weekly revenue of scooters is approximately normally
distributed with a standard deviation of $50 (variance of 2,500
squared dollars).
Find values a and b such that (i) the probability is 0.9 that the
sample standard deviation s will be between a and b and (ii) the
probability is 0.05 that s will be less than a. What is the value
of a? what is the value for b?