Dispensing Coffee. 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?

Question

Dispensing Coffee. 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?

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