Good day I would like some detailed explanations for the following quantative methods exercise

Which one of the following represents a binomial random variable? Select one: a. number of girls taller than 1.68 metres in a random sample O b. time it takes a randomly selected student to complete a multiple choice exam O c. number of CDs a randomly selected person owns O d. number of randomly selected textbooks bought from 60 textbooks this termAmoy is the Project Manager of a project that must be completed by end of September 2024. The completion time for this kind of project is normally distributed, with an average of 15 months and a standard deviation of 3 months. Assuming that the project will start at the beginning of a month, what is the latest (month & year) can Amoy start this project to have a 95% certainty of meeting the September 2024 deadline? Select one: O a. February 2023 O b. April 2023 c. December 2022 O d. May 2023A project has estimated optimistic (a), most likely (m) and pessimistic (b) times for activity D as 7, 8 and 14 days, respectively. What is the mean AND variance for activity D, respectively (to 1 decimal place): Select one: O a. 8.8 and 1.2 O b. 8.5 and 0.7 O c. 8.8 and 0.7 O d. 9.7 and 1.4The following are properties of a set of random variables, EXCEPT: Select one: a. The sum of the associated probabilities is equal to 1. O b. Can either be discrete or continuous. O c. Value must be between 0 and 1 O d. The expected value can be calculated