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STAT 319 hob. & Slal. for Eng. & Scientists
KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DEPARTMENT OF MATHEMATICAL SCIENCES
DHAHRAN, SAUDI ARABIA
STAT 319: Probabili ty & Statistics for Engineers & Scientists Semester 141
First Major Exam Wednesday October 15, 20 14
6:00 - 7:00 pm
Please circle your instructor nrune:
Abbas Al-Sabah Al-Sawi
Anabosi Malik Saleh
Section # : Selial #:Name:
Question No
1
Full M arks
6
Marks Obtained
2 6
3 14
4 6
5 13
Total 4S
2 STAT 319 Prob. & Stat. [or Eng. & Scientists
Q1. (6 marks) A manufacturing firm employs three analytical plans for the design and development of a particular product. For cost reasons. all three are used at different times In fact, plans 1 and 2 are used fo r 30% and 20% of Ule products, respe tively. The defect rate for the plans 1, 2, and 3 are 1%, 3%, and 2% respectively. 1f a random product was observed and found to be defecti ve, which plan was most likely used and thus responsible?
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I PLllI J :: o. S
I \'(D\m) =a.dL
Q2. (2+2+2 marks) Is each statement below True or False? Give an explanabon.
a. The probabil ity that a mineral sample will contain silver i 0.38 and the probability that it willF not contain si lver is 0.52.
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b. The probability that a student will get an A in STAT 319 is 0.3, and the probability that he will F get either and A or a B is 0.27.
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r- A company is constructing two buildings ; the pr bability that the larger one will be completedc. on time is 0.3 5 and the probability that both wi ll be completed on time is 0.42.
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f LAn 8') <. p ( ,A) 8< fC-A- G)'::; {)(BJ
STAT 319 Prob. & Stat. for Eng. & Scientists 3
Q3. (2+2+2+8 marks) Errors in an experimental transmission channel are found when the transmission is checked by a certifier that detects missing pulses. The number of errors found in an eight-bit byte is a random variable with the following cumulative distribution function:
O, X< l } F(x) = 0.8, 1 :5 x < 4
0.9, 4 :5 x < 7{ 1.0, 7 :5 x
Determine each of the following probabilities .
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G) b. P(X> 7) =
Ft 1:)) =. F(4)::0@ c. P(X:SS ) =
d. Find the mean and variance of the number of errors fo und in an eight-bIt byte.
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Q4. (4+2 marks) Assume that flaws per sheet of glass can be represented by a Poisson di stribution, wi th an average of 0.7 flaws per sheet.
a. What is the probability that randomly selected two sheets of glass have more than one fl aw?
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~ I~ ~ =- - e [I + ,.ttJ / -2 ·lf e ~ ~ rO .LjO~~" b. What is the mean number of flaws per 12 sheets?
STAT 319 Prob . & Stat. for Eng. & Scientists 4
Q5. (4+4+3+2 marks) Twenty five perc nt of all households ha e a DVD player. a. If you select 20 houses at random, what is the probability that at least three of them have a DVD
player? ~ r~ o· 2S' I n =2,0, I< ': #:1 ~O'J..s ') w D\J 1) =t:> x: B(20/o.~) -t n :>t '2 - .:>.
(S) }(~) -= ~o '-~ 0 '25 o·~ ~ /!X. 01 I, ~ - --/10
?(X~3) l-p(X<'~) \-peX ~~) )- [t((J) -t- f(IJ ~ f( 10
'<-0 '1 c t. , Y7 ~ \ "..r ) -T 2 CJ ~ ( 0 l 5' CI·1 C; + 2 0 1- CJ. 7 C CI '?J t;' - Jl ::: \ _ L0.0C?, '2-1- () fo 2.lt -f-C 6~~] =@. Cj or~JI'r"\
b. If the household were checked one by one, what is the probability that the first household, that \U has a DVD player, is the fifth ? _, 5 +-- '
Q let X 4t ~ lO~) (h ('Ie. Of LAvt-l-r'" +1-u-1- w(~ 4 DV b-
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s-IP{i= c;) = t(5)=d5 .g)(IJ.:/-) =(O.O,!-'II] GJ
c. Given that in a randoml y selected block there are 16 houses, what is tbe probability that 3 houses would have a DVD player, in a sample of 8 houses randomly selected from that block?
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6) /6 C2. Ii' JtX.+h ~CU p( i<' ) ~ 4 C1 . I~C C:-/I :: 12 9 1) =f 0 ·l l.(/:,?, J
d. Referring to part c before, what is the expected number of houses that would have a DVD player?