A coffee machine is supposed to dispense 6 fluid ounces (fl oz) of coffee into a paper cup. In reality, the amounts dispensed vary from cup to cup. In fact, the amount dispensed, in fl oz, is a variable with density curve y = 2 for 5.75 < x < 6.25, and y = 0 otherwise.
a. Graph the density curve of this variable.
b. Show that the area under this density curve to the left of any number x between 5.75 and 6.25 equals 2x − 11.5.
What percentage of cups dispensed by this machine contain
c. Less than 6 fl oz?
d. Between 5.9 and 6.1 fl oz?
e. At least 5.8 fl oz?