Suppose that we want to install new photocells for a house in Calgary. There are 2 types available in market. Assume that the life length of the photocell from manufacturer 1 have normal distribution with an average of 15 years and variance of 25. Also assume that the life length of the photocell from manufacturer 2 have normal distribution with an average of 20 years and variance of Q. a. If we want to use the photocell for 20 years, which manufacturer would be preferred? (Compare using calculated probabilities} b. If we want to use it for 17 years, which manufacturer is preferred? (Compare using calculated probabilities) Now. we want to install the photocell in Vancouver. Based on data, the number of rainy days in Vancouver is 192 per year. Assume that this probability does not depend on the season and is constant during the year. Also assume that the photocell only works on sunny days. (there are 365 days in a year and the weather is either sunny or rainy) c. What is the probability that the photocell work on a randomly selected day? d. Assume that we randomly select 10 days in a year, what is the probability that the photocell works exactly 5 days of the week. Now assume that the number of rainy days in Vancouver follows a Poisson distribution and answer the following questions: e. What is the probability that the photocell does not work for at least 2 weeks? f. What is the probability that the photocell does not work for 3 days? g. What is the expected time between 2 none working days for the photocell