statistics

(a) (b) (C) ((0 TEST 2 A survey from XYZ limited found that 35% of teenage consumers receive their spending money from part time jobs. If 8 teenagers are selected at random, (i) nd the probability that less than 2 of them receive their spending money from part time jobs. (3 marks) (ii) nd the probability that 4 to 6 of them receive their spending money not from part time jobs. (4 marks) The mass of a small loaf of bread is normally distributed with a mean of 500g and a standard deviation of 20g. (i) Find is the probability that a randomly chosen loaf has a mass of 495g to 497g. (4 marks) (ii) Find is the probability that a randomly chosen loaf from a selected 16 loafs of bread has a mass in between 498g to 502g. (4 marks) After watching a number of children playing games at a video arcade, a teacher estimated the following probability distribution of X, the number of games played per visit. X 1 2 3 4 ] 5 P(X = x) 0.00 0.10 0.40 0.30 J 0.20 (i) Find the probability of a child who plays more than 2 games per visit. (2 marks) (ii) Find the mean and standard deviation of the number of games played per visit. (5 marks) Car that arrives at a toll plaza follows a Poisson distribution with an average of 4 cars in every 2 minutes time interval. (i) Find the probability that there will be exactly 3 car that arrives at a toll plaza in a minute. (3 marks) (ii) Find the probability that there will be at most a car in the next 3 minutes