(a) A marketing company is conducting an experiment in which participants are to taste one of two different brands of orange juice. Their task is to correctly identify the brand tasted. A random sample of 120 participants is taken and it is assumed that the participants have no ability to distinguish between the two brands. (i) What is the probability that the sample percentage of correct identifications is greater than 80? 1 mark (ii) What is the probability that the sample will have between 50% and 60% of the identifications correct? 1 mark (b) A survey conducted by Skyscanner found that the average time of plane departure from Brisbane airport is normally distributed, with a mean of 36 minutes and a standard deviation of 3 minutes. What value does the upper 10% of the time exceed? 1 mark (c) The transport association conducted a survey on the speed of vehicles travelling around the neighbourhood. It is found that the speed of vehicles varies uniformly between 55 km/hour and 62 km/hour in the 60 km/hour zone. What is the probability that the speed of vehicles will be less than 58 km/hour?