[ill x = j .JY (y - 3),

11-12 Find the centroid of the region bounded by the given curves.
II. y = ~x, y = j";
12. Y = sinx, y = 0, x = 7[/4, x = 37[/4
y
2
1
-2 0 3 x
15. Find the volume obtained when the circle of radius 1 with
center (l, 0) is rotated about the y-axis.
16. Use the Theorem of Pappus and the fact that the volume of a
sphere of radius r is ~'TTr 3 to find the centroid of the semicircular
region bounded by the curve y = )r 2 - x 2 and
the x-axis.
Find the consumer surplus when the sales level is 100.
18. After a 6-mg injection of dye into a heart, the readings of
dye concentration at two-second intervals are as shown in
the table. Use Simpson's Rule to estimate the cardiac output.
I
t c(t) t c(t)
0 0 14 4.7
2 1.9 16 3.3
4 3.3 18 2.1
6 5.1 20 1.1
8 7.6 22 0.5
10 7.1 24 0
12 5.8
is a probability density function.
(b) Find P(X < 4).
(c) Calculate the mean. Is the value what you would expect?
20. Lengths of human pregnancies are normally distributed
with mean 268 days and standard deviation 15 days. What percentage
of pregnancies last between 250 days and 280 days?
21. The length of time spent waiting in line at a certain bank
is modeled by an exponential density function with mean
8 minutes.
(a) What is the probability that a customer is served in the first
3 minutes?
(b) What is the probability that a customer has to wait more
than 10 minutes?
(c) What is the median waiting time?