(a)The local police station found that the speed of vehicles travelling around the suburb in the 60 km/hour zone varies uniformly between 55 km/hour and 62 km/hour. What is the probability that the speed of vehicles will be less than 58 km/hour?

(b)A marketing company is conducting an experiment in which participants are to taste one of two different brands of coffee. Their task is to correctly identify the brand tasted. A random sample of 150 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 70?

(ii) What is the probability that the sample will have between 40% and 50% of the identifications correct?

(c) A survey conducted by Burwood train station found that the average time of train arrival at the station is normally distributed, with a mean of 36 minutes and a standard deviation of 3 minutes. What value does the upper 5% of the time exceed?