Answer :
Answer:
(a) 13 ounces.
(b) 1.732 ounces.
(c) 0.5
(d) 0.33
Step-by-step explanation:
Given : The amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces. So, a=10 and b=16.
(a) The average amount of water dispensed by the machine = (a+b)/2 = (10+16)/2 = 13 ounces.
(b) The standard deviation of the amount of water dispensed = [tex]\int\limits^a_b {\frac{(b-a)^{2} }{12} } \, dx \\[/tex] = √36/12 =√3 = 1.732 ounces.
(c) P (13 or more ounces will be dispensed in a given glass) = [tex]\int\limits^a_b {f(x)} \, dx[/tex] = [tex]\int\limits^b_a {\frac{dx}{b-a} } \, dx[/tex] = 0.5
(d) P (between 12 and 14 ounces will be dispensed in a given glass) = ( here a=12 and b=14.) [tex]\int\limits^a_b {f(x)} \, dx[/tex] = [tex]\int\limits^b_a {\frac{dx}{b-a} } \, dx[/tex] = 0.33