Question 752937
Let


L = lower bound of confidence interval


U = upper bound of confidence interval



We're given that L = 3.15 and U = 3.45


So


L = X - E


3.15 = X - E



and


U = X + E


3.45 = X + E


The equations are 


3.15 = X - E
3.45 = X + E


Add them up to get


6.60 = 2X + 0E


6.60 = 2X


2X = 6.60


X = 6.60/2


X = 3.30


The sample mean is xbar = 3.30


3.15 = X - E


3.15 = 3.30 - E


3.15 - 3.30  = -E


-0.15  = -E


-E = -0.15


E = 0.15


The margin of error is 0.15



So the sample mean is $3.30 and the margin of error is $0.15 (15 cents)