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?

J PC If) =0-1­

PeD'1I"'j: a· 0 ~

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.

\ -1'( A ) -::p o.~

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.

P l A {) B) ~ PCA)

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.

'5 \lI\e~ An ~ c.. A ";r A(\RC B =IJ

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 .

6) a. P(X" 4) ~ F ( If) : .n; ,_ pC i <. T) w:.1 - ( 1-) \- , - ~

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.

6)f( I)" O· - cJ .:. (,) .~ I r 'fI .=c 0 .'\ - 0 t = ., '/ f ( :1) -= 1- I • 'I::. o· ,

'X- ft"J rD l.:p EU):. I fc.:) ~ [3J@ ~~~~~~~~~--~~ ~~

(j~. ~ _(x2) _ :x- ~ :) - 1 ­()'-f I- b o~ \J; VCj)~ F-LX2J _/~L{i) m

6 .. \ tr1 4 4 ~ '7-'1 - \·4 -= 6- b1j::t ). , 1-, ~ ::p1­

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?

LeJ X: #-c vV + - 'A ~ Po rAt) (w"'e~ ~:: 0·:r-Tf~=P fc.x.j:: e 1£1 '.4 x. _ r;, I I - CD- A I t . ­

L;J ?C. ~ ~

p ( X;:> I '):; I - pC X ~ I) =:: I - L~0) '1 t ( J) J (0 (0)

~ 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-

X ~ G.t C.L2S) =()Q.f-(xj - b_'2S-)(O:~C;-).::r-~ .?l_ I / L/ --­

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?

N =- Ib, VL =- ~ I X =3 ! K ~ 0 ~ 5 ~I

0L~+ X' U= of hov~~J w (~ DiJ f) 1-" &f fa pi of ~oJ, If:,

:4:> ~C~j= LfCx - 12.C.~_ -=.p

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?