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KING FAHD UNIVERSITY OF PETROLEUM & MINERALS
DEPARTMENT OF MATHEMATICS & STATISTICS
DHAHRAN, SAUDI ARABIA
STAT 319: PROBABILITY & STATISTICS FOR ENGINEERS & SCIENTISTS
Final Exam, Semester 093, Date: August 25, 2010
Time: 9.00 - 11pm
ID#
NAME:
SECTION #
Please tick the name of your instructor
Instructor
H. Muttlak
M. Malik
Sections
2 and 3
1 and 4
1. Do turn off the mobile and leave it aside.
2. Keep your answers to at least 3 decimal places.
3. Check that the exam paper has questions.
Q
Marks
1
12
2
12
3
10
4
19
5
12
6
15
Total
80
Marks
Obtained
Notes
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Q1. ( 4+4+ 2+ 2= 12 Marks) A machine produces metal rods used in an automobile
suspension system. A random sample of 15 rods is selected, and the diameter is
measured. The resulting data (in millimeters) are as follows:
8.24, 8.25, 8.20, 8.23, 8.24, 8.21, 8.26, 8.20, 8.23, 8.19, 8.28, 8.24, 8.26, 8.23
8.25
a. Find a 95% two-sided confidence interval on mean rod diameter.
b. Is there evidence that the mean yield is not 8.22 mm? Use 5% level of
significance.
c. What is the P-value for this test?
d. What assumption is required to do part a, b, and c?
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Q2 (5+4+3=12 Marks) A semiconductor manufacturer produces controllers used
in automobile engine applications. The semiconductor manufacturer takes a
random sample of 200 devices and finds that 8 of them are defectives.
a. The customer requires that the process fallout or fraction defective at a critical
manufacturing step not exceed 0.06, can the manufacturer demonstrate process
capability at this level of quality using α = 0.05.
b. Estimate the population proportion using 98% confidence level..
c. Determine the sample size required to estimate the population to be with in ±
.02 and with 99% confidence.
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Q3. (2+ 5+ 3=10 Marks) The diameter of steel rods manufactured on two
different extrusion machines is being investigated. Two random samples of sizes
n1=15 and n2 = 17 are selected, and the sample means and sample variances
are X 1  8.73 , S 12  0.35 , X 1  8.68 , and S 22  0.40 respectively. Assume that
the  12   22   2 but unknown and that the data are drawn from a normal
distribution
a. Obtain the pooled estimate of the unknown variance
b. Construct a 95% confidence interval for the difference in mean rod diameter.
c. Using your results in part b, test the claim that no difference between the two
extrusion machines.
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Q4. (6+ 5+ 5+ 4= 19 Marks) An article in the Tappi Journal (March, 1986) presented
data on Na2S concentration (in grams per liter) and paper machine production (in tons
per day). The data (read from a graph) are shown as follows
n  13,  yi  632,  yi2  31128,  xi  12207,  xi2 11529419,  xi yi  598098
a. Fit the regression line and find the fitted value of y corresponding to x = 910
and the associated residual.
b. Test for significance of regression using p-value. Assume α = 0.05.
c. Find a 99% confidence interval of Mean Na2S concentration when production
x = 910 tons/day
d. Calculate R2 for this model and provide a practical interpretation of this
quantity.
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Q5 ( 5+ 4+ 2+ 1= 12 Marks) A manufacturer of video display units is
testing two microcircuit designs to determine whether they produce
equivalent current flow. Development engineering has obtained the following
data:
Design 1
b.
c.
d.
x1  24.2
s12  10
s 22  20
x 2  23.9
Determine whether there is any difference in the mean current flow between
the two designs. Report your p-value
Construct a 95% confidence interval for the difference between the two
population means.
State the assumptions that need to answer the above two parts.
What is your final conclusion about the two designs?
Design 2
a.
n1 = 35
n2 = 40
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Q6. ( 15 Marks) Answer any 3 from the following short questions.
a. The time between calls to a bank is exponentially distributed with a mean time
between calls of 15 minutes. What is the probability that there are no calls
within a 30 minute interval?
b. An electronic product contains 10 integrated circuits. The probability that any
integrated circuit is defective is 0.01, and the integrated circuits are
independent. The product operates only if there are no defective integrated
circuits. What is the probability that the product operates?
c. The fill amount of mineral water bottles is distributed, with a mean of 4.0
liters and a standard deviation of 0.08 liter. If you select a random sample of
31 bottles, what is the probability that the sample mean will be between 3.99
and 4.0 liters?
d. If a quality control engineer wants to estimate the mean life of light bulbs to
within  20 hours with 95% confidence and also assumes that the population
standard deviation is 100 hours, how many light bulbs need to be selected?