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STAT 211 Business Statistics I – Term 103
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
DEPARTMENT OF MATHEMATICS & STATISTICS
DHAHRAN, SAUDI ARABIA
STAT 211: BUSINESS STATISTICS I
Semester 103
Major Exam Two
Saturday August 6, 2011
Allowed time 90 minutes
Instructor
section number
Musawar Amin Malik
Sec 2: (09:20 –10:20)
Name:
Student ID#:
Serial #:
Directions:
1) You must show all work to obtain full credit for questions on this exam.
2) DO NOT round your answers at each step. Round answers only if necessary at your final
step to 4 decimal places.
3) You are allowed to use electronic calculators and other reasonable writing accessories that
help write the exam. Try to define events, formulate problem and solve.
4) Do not keep your mobile with you during the exam, turn off your mobile and leave it aside
Question No Full Marks Marks Obtained
Q1
10
Q2
7
Q3
5
Q4
5
Q5
6
Q6
16
Q7
6
Q8
5
Total
60
1
STAT 211 Business Statistics I – Term 103
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Question One (2+4+4 = 10 points)
The following table contains the probability distribution for X = the number of days required for a project
completion. A contractor is going to bid the project.
X
10
11
12
13
14
P(X)
0.2
0.3
0.25
0.15
0.1
a. Find the probability that the number of days required to complete the project is less than 13.
The contractor’s profit is Y = 200(12 + X).
b. Find the expected profit of the contractor.
c. Find the variance of Y.
Question two (3+4 = 7 points)
A particularly long traffic light on your morning commute is green 20% of the time that you approach it.
Assume that each morning represents an independent trial.
a. Over 20 mornings, what is the probability that the light is green on exactly four days?
b. Over five mornings, what is the probability that the light is green on at least two days?
STAT 211 Business Statistics I – Term 103
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Question three (5 points)
Contamination is a problem in the manufacture of optical storage disks. The number of particles of
contamination that occur on an optical disk has a Poisson distribution, and the average number of particles
per centimeter squared of media surface is 0.1. The area of a disk under study is 100 squared centimeters.
Find the probability that 12 particles occur in the area of a disk under study.
Question four (5 points)
A batch of parts contains 100 parts from a local supplier of tubing and 200 parts from a supplier of tubing in
the next state. If five parts are purchased randomly, what is the probability that there are three parts from the
local supplier?
Question five (6 points)
In a large corporate computer network, user log-ons to the system can be modeled as a Poisson process with
a mean of 2 log-ons per minute. What is the probability that the time until the next log-on is between 2.5
and 3.5 minutes?
STAT 211 Business Statistics I – Term 103
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Question six (4+4+4+4 = 16 points)
The fill volume of a soft drink cans filled by a certain machine is normally distributed with mean 12.05 oz
and standard deviation 0.04 oz.
a. What is the fill volume that 90% of the cans will exceed?
b. What is the probability of those cans which contain less than 12 oz?
c. If you select 5 cans what is the probability that more than one of them will have content less than 12
oz?
d. Find the probability that a random sample of 16 cans will have a sample mean volume at least 12.09
oz.
STAT 211 Business Statistics I – Term 103
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Question seven (6 points)
PVC pipe is manufactured with a mean diameter of 1.01 in and standard deviation 0.003 in. Find the
probability that a random sample of 36 sections of pipe will have a sample mean diameter greater than 1.009
in.
Question eight (5 points)
Yahoo HotJobs reported that 56% of full time office workers believe that dressing-down can affect jobs,
salaries, or promotions. Suppose that you take a sample of 100 full-time workers. What is the probability
that the sample proportion will be contained between 0.60 and 0.65?
STAT 211 Business Statistics I – Term 103
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Some Useful Formulas
 1 
  t x e  t
,  t
Poisson: P  x  
 Binomial: P  x   C xn



n x
x
x!
Hyeprgeometric: P  x  
C
N X
nx
N
n
C
C
Exponential: P  0  x  a   1 
e

x

X
x
,   E  X   n  ,   n 1   
,   t
 N  A  A 
 n  x  x 
 

N 
n
 