6.80 During an 8-hour shift, the proportion of time X that a sheet-metal stamping machine is down for maintenance or repairs has a beta distribution with and .That is, The cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by

.

a Find the mean and variance of C.

b Find an interval in which C will lie with probability at least 0.75.