Melatonin is widely employed to help people with insomnia fall asleep. Assume the probability distribution of X, the time (in minutes) it takes to fall asleep after taking the melatonin tablet is given by
f(x)= { 0.1-0.005x , 0?x?20
0, otherwise}
a) Determine the probability that it takes between 5 and 15 minutes to fall asleep after taking tablet
b) Determine the mean and standard deviation of the number of minutes its takes to fall asleep after taking the tablet