6.7 The proportion of time, during a 40-hour workweek, that an industrial robot was in operation was measured for a large number of weeks, and the measurements can be modeled by the probability density function If X denotes the proportion of time this robot will be in operation during a coming week, find the following:

a P (X  12)

b P (X  12|X  14)

c P (X  14|X  12)

d Find F(x) and graph this function. Is F(x)

continuous?