stats question

6. Everyday during the pandemic, Stella decides to take a walk in the UCI Wildlife Preserve with probability 0.7, and she decides to stay indoors with probability 0.3. If she takes a walk in the Wildlife Preserve, the duration of the walk (in minutes) is a continuous random variable with pdf and f (a) : 0 if :13 50. Dene W : 1 if Stella decides to take a walk on a randomly chosen day and W : 0 if she stays indoors. Let X denote the duration of Stella's walk in minutes on that day. (If she stays indoors, then X : 0.) (a 10pts) Verify that E(X|W : 1) : (100/3) log(5/2). Show steps. (b 10pts) Compute E (X ) using the law of total expectation. (c 10pts) In 2020 so far, Stella has taken a walk in the Wildlife Preserve on a total of 227 days. Set up notation, state assumptions, and use the CLT to approximate the probability that the average duration of these 22? walks exceeds 30 minutes. You may need the following results concerning the standard normal distribution. If Z is a standard normal random variable, then P(|Z|