Question

QUESTION 1 [10] It is known that 80 % of all students have their own laptops, thus in a random sample of eight students, find the following probabilities: 1.1) That exactly seven students will have their own laptops. (3) 1.2) That at least six students will have their own laptops. (4) 1.3) That at most five students will have their own laptops (4) QUESTION 2 [11] The number of accidents that occur on an assembly line have a Poisson distribution with an average of five accidents per week. 2.1) Find the probability that exactly two accidents will occur in a week. (3) 2.2) Find the probability that a particular week will be accident free. (3) 2.3) Find the probability that at least three accidents will occur in a week. (3) 2.4) If the accidents in different weeks are independent of each other, find the expected number of accidents to occur in a year. (2) QUESTION 3 [9] The time it takes a student to complete an assignment is normally distributed with mean 45 minutes and a standard deviation of 7 minutes. Find the probability that it takes the following lengths of time for a student to complete an assignment. 3.1) Between 45 and 56 minutes. (3) 3.2) Less than 33 minutes (3) 3.3) More than 29 minutes (3)

Answer 1