1. (a) 0.02
(b) 0.38 + 0.43 = 0.81
(c) 0.43/0.45 = 0.9555
(d) Not independent. 0.9555 not= 0.60
(among other reasons)
2. (a) 0.154 + 0.15 + 0.189 = 0.493
(b) 0.2 / 0.811 = 0.2466
3. By CLT, Z = 0.7852 -> prob=0.7806
4. (a) 1/0.15 = 6.666
(b) 1-0.85^8 = 0.7275
5. (a) rate=5/30, p=0.84648 = exp(-5/30)
(b) rate=10/30, p=0.71653
6. (a) E(large) = 5*12/19 = 3.15789
(b) p(3 large)=C(12,3)*C(7,2)/C(19,5)=0.397317
7. (a) P(X>180)=P(Z>1)=1-0.8413=0.1587
(b) P(X<t)=0.875 -> (t-165)/15=1.15 -> t=165+/-17.25
or 162.75 < t < 197.25
(c) E(total)=825, Var(total)=5*15^2
P(total<850)=P(Z<0.745) = 0.772 (approx)
8. (a) P(X>6) = exp(-6/4) = 0.2231
(b) 1/0.2231 = 4.48 (geometric)
(c) 2.7725
(d) 0.5438 = exp(-10/4)(1+10/4+(10/4)^2/2)
(e) X=length, area=x^2/(4*pi)
P(Area<y)=P(X<sqrt(4*pi*y))=1-exp(-sqrt(4*pi*y)/4)
9. (a) 1.5 min
(b) 0.3