The population mean of a company's racing cycles is 9.9 kg with a population standard deviation of 0.4 kg. If the distribution is approximatively normal:

a) determine the percentage of bicycles with weight less than 9.4 kg. (5 points)

b) determine the percentage of bicycles with weight between 9.4 and 10.2 kg (5 points)

c) determine to which value the standard deviation should be adjusted (without changing the mean) to insure that 99.70% of the bicycles weights less than 10.4 kg. (10 points)