Problem 2 [21 points (5, 5, 5, 6)]: Yoga Revenue A yoga studio is trying to estimate total class sales for the next year. They assume that: ii iii iv 0 Between 10 and 14 peOple attend each class (uniformly distributed) 0 Each person pays 15 dollars per class. a Total attendance between any two classes is independent a They host 2 classes a day, 5 days a week for the 50 weeks in the year (500 total classes) We'll estimate the total sales using a normal distribution. Why is it reasonable to use a normal distribution? Write one or two sentences which mentions any theorems and explicitly addresses any assumptions they require. Let a: be a random variable deseribing the number of people who attend a single class: E[a:] =Zx,P(X=m,-) = (:10+ :11+ :12+ :13+ :14) = 12 z" and: 1 1 1 1 1 2 2 _ _ _ 2 _ 2 _ 2 _ 2 _ 2_ E[w1= 2i ,w1P(Xa=1)=510 +511 +512 +513 +514 146 so that: Va'r(m) = E[a:2] E[;r:]2 = 146 144 = 2 Compute the expected value and variance of the revenue, 7' = 15$, raised in a single clas Estimate the expected value and variance of the revenue generated over the whole year of classes. To pay its instructor, utilities and rent the studio needs to generate at least 89,000 dollars. Using the model above, compute the probability that the studio is able to cover its costs. (Hint: you'll need 'scipy.stats.n0rm')