6.What is the probability that an engine is unacceptable and that it was manufactured eithe
a)0.04%b)3.93%c)67.86%d)71.79%P(U ∩ [M1 ∪M2) ] = P(U ∩ M1) + P(U ∩ M2) = 30/1400 + 25/1400 =55/14

efective?

ured at M1 or M2?
ptable?
er at factory M1 or M2?
400

Questions 7-13
joint
D
0.1
nD
0.9
A/D
0.1
0.01
B/D
0.2
0.02
C/D
0.7
0.07
A/nD
0.6
0.54
B/nD
0.3
0.27
C/nD
0.1
0.09
P(A)
0.55
P(B)
0.29
P©
0.16
7)
b)
0.16 P©
8)
c)
0.84 P(AorB)
9)
e)
0.4375
10)
c)
0.0563
0.5625
11)
c)
0.9437 0.05631351
12)
c)
0 P(A)
0.8 P(D)
0.05
13)
a)
0.76

Questions 14-19
Last year
Days
3
Shots
2
Value
5000
Answer
Shots/day
0.6666667 lambda
14)
c)
Expected rev
3333.3333
15)
b)
Poisson
0.1443048 right
0.1140927 wrong
16)
e)
SD=sqrt(lambda)*$
4082.4829
17)
d)
2*SD
8164.9658
18)
c)
Risk of 4 days
0.6123724
Risk of 1 day
1.2247449
Ratio
2 even if they get the SD wrong in (3), this answ
19)
c)
Rev-Cost
11333.333

wer should be OK

Questions 20-29
20. Given
n
7
p
0.75
Solution: d
21. Expected Value
Binomial, therefore:
E(X)=np
5.25
1.75
Solution: b
22. Standard Deviation
q
0.25
sd
1.14564392
Solution: b
23. Probability
x
3
p(x=3)
0.058
0.058
Solution: b
24. Approach
Solution: Poisson
c)
25. Probability - 5 min
l
6
x
1
p(x=0)
0
0.002
p(x=1)
1
0.015
0.017
Solution:
0.017
c)
26. Probability - 2 min
l
2.4
x
3

p(x=0)
0
0.091
p(x=1)
1
0.218
p(x=2)
2
0.261
p(x=3)
3
0.209
0.779
0.779
Solution:
0.221
c)
Normal Question
27. Given:
x
7.5
mu
7.2
sd
2.3
Solution: c
28. z calculationa0.130b-0.130c-3d3

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- Fall '05
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- Probability theory, Hungary, M3 Half-track, M2 Browning machine gun