3. The journey times, in i'niJ'mtes1 of three students to travel to LSE [pre-Covidi] can be regarded as independent and normally distributed random variables with means and standard deviations as given in the following table: Student Mean Standard deviation Departure time A 139:30 B 09:10 '3 09:20 In order to attend a 10:00 lecture. the students leave home at the times shown in the right-hand column of the table. Let A. B and C be the random variables denoting the journey times1 in minutes1 of students A, E and C, respectively. {a} Find the probabilities of the following events: 1. Student A is late for the lecture. ii. Student A arrives at LSE before Student E. iii. At least 1 student is late for the lecture. iv. All 3 students are late for the lecture. given that at least one student is late for the lecture. v. Student C is late for the lecture, given that exactly one student is late for the lecture. [b] At what time should Student 13 leave home if there is to be a 2.5% chance of her being late