University of Toronto
Department of Materials Science and Engineering
Engineering Statistics MSE 238h1s
FOURTH QUIZ , 10 th FEBRUARY 2005, 14:15-14:45
QUESTION 1 ( MARKS 30 )
Let P(A) = 0.4 and P(A

B) = 0.7 What is P(B) if
(a) A and B are independent

P(A

B)= P(A)P(B)
P(A

B)=P(A)+P(B)-P(A

B)

0.7=0.4+P(B)-0.4.P(B)

(b) A and B mutually exclusive

P(A

B)=0
P(A

B)=P(A)+P(B)-P(A

B)

0.7=0.4+P(B)

P(B)=0.3
QUESTION 2 ( MARKS 35 )
P(B)=0.5
Find the probabilities of getting
(a) eight heads in a row with balanced coin

(1/2)
8
(b) three 3’s and then a 4 or a 5 in four rolls of a balanced die 
(1/6)
3
.(2/6)
(c) five multiple-choice questions answered correctly, if for each question the probability of answering it correctly is 1/3

(1/3)
5
QUESTION 3 ( MARKS 35 )
A company is analyzing the compressive strength of a new material. Compressive strength is normally distributed with
 2
= 1000(psi)
2
. A random sample of 12 specimens has a mean compressive strength of x

3250 psi
(a) Construct a 95% two-sided confidence interval on mean compressive strength.
Z 
/2
= Z
0.025
= 1.96

3250-1.96(1000/12)
0.5

3250+1.96(1000/12)
0.5
)

3232.11

3267.89
(b) Construct a 99% two-sided confidence interval on mean compressive strength. Compare the width of this confidence interval with the width of the one found in part (a).
Z 
/2
= Z
0.005
= 2.58

3250-2.58(1000/12)
0.5

3250+2.58(1000/12)
0.5

3226.5

3273.5
This interval is longer because it is calculated with a higher level of confidence.