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Stat 319: Statistics for Engineering
Quiz # 4, 18/ 11 /2006, Instructor: Prof. Hassen A. Muttlak
Name:
ID#
FORM A
Section
1. (3 points) Let Z be a standard normal random variable compute the following:
a.
P (1.21 Z  2.7) 
b. P ( Z  1.17) =
c. Find c such that P (0  Z  c )  0.195
2. (3 points) Let X be a normal random variable with mean 85 and standard deviation 10,
compute the following:
a.
P (X  80) 
b. P (85  X  95) 
c. Find c such that P (X  c )  0.15
3. (4 points )Let X denote the amount of space occupied by an article placed in a 1- ft3
packing container.
And having the following function:
cx (1  x ), 0  x  1
f (x )  
otherwise
0
a.
b.
c.
d.
Find the value of c which make (x) a probability density function.
What is the probability that the amount of the space occupied is more than 0.85?
Find the mean of the amount of the space occupied.
Find the 75th percentile of the distribution.
Stat 319: Statistics for Engineering
Quiz # 4, 18/ 11 /2006, Instructor: Prof. Hassen A. Muttlak
Name:
ID#
FORM B
Section
1. (3 points) Let Z be a standard normal random variable compute the following:
a.
P (1.31 Z  2.8) 
b. P ( Z  1.27) =
c. Find c such that P (0  Z  c )  0.295
2. (3 points) Let X be a normal random variable with mean 85 and standard deviation 10,
compute the following:
a.
P (X  81) 
b. P (85  X  94) 
c. Find c such that P (X  c )  0.17
3. (4 points )Let X denote the amount of space occupied by an article placed in a 1- ft3 packing
container.
And having the following function:
cx (1  x ), 0  x  1
f (x )  
otherwise
0
a.
b.
c.
d.
Find the value of c which make (x) a probability density function.
What is the probability that the amount of the space occupied is more than 0.65?
Find the mean of the amount of the space occupied.
Find the 25th percentile of the distribution.