MATH 204 Exam 2, Fall 2002
American University of Beirut · Mathematics for Social Sciences II · 5 pages
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PART I For the following 16 questions,use the ANSWER TABLE(above)
and fill in your choice of the correct letter ab,c.d ore:
Given the following data set: 8,10,14,14,25,27,31,31,31,49 Answer questions 1-2-3-4 .
1. The mean is; a
a. 18,7 b26 (G24 d. 19.2
2.The median is:
a. 41 b. 31 (426
%, The range is :
a. 51 (1) . d. 49
4. The mode is:
(2.31 b. 14 a 4 d. 10
Given a normally distributed random variable , with mean 65 and standard deviation 2.4.
Answer questions 5 and 6.
5, Find P(64.4<X<68.6). +) 2
a. 0.3345 b. 0.4332 (« 0.5319 d. 0.6521
A
6. To the left of what value of X is the area under the normal curve equal to 0, 0170?
a 49.912 ; b. 59.912 (c 70.088 d, 60.088
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- PART II Answer in the sp2ze provided: LIBRARY
2 BELRUT
|. Evaluate: r=fax+2 8 ar _
x x
Lo: SUnax + {4x - ,
2x745 KnxX 43 46
ye
(e+ las
x
Il. Evaluate: K=[-—— |
(e* -Inx)
Pa
> (feed yo
oe OM €.x)°
waka. . JX
Na 7 ¥AX }
oe
LAE mie + fowl
" yo) pe cn
) LA 7
“
eek eA
_ EnjCe “ Lax : = “a
YL’
Consider the following probability distribution table: OF RBeERUT
“TX [PX .
0.3
50 | 0.5
i 60 10.1
70 {04
Answer questions 7 and 8.
7. What is the mean of the distribution?
(250 bo 55 82 d. 54
8. What is the standard deviation? (Answer is rounded).
Four dice of different colors are thrown.Answer the questions 9-10-11
9. What is the probability that there will be exactly two fives?
a, 5/216 (Besieie c, 1/36 d. 5/36
10.What is the Tiean number of fives expected te be?
a. 2/3 b. 2 c. 3/2 d. 1/6
11.What is the standard deviation of the number of fives expected to be?(Answer is rounded).
{4.0.55 b. 0.65 c. 0.75 d. 0.45
\ + 12.The function describing the marginal profit from producing and selling a product is:
c MP= -2x+800
Where x equals the number of units and MP is the marginal profit measured in dollars . When
100 items are produced and sold , total profit equals $85,000.Determine the profit when 200
items are produced and sold.
a. $120,000 b. $125,000 —. $130,000 (a) $135,000
3.The value of an asset is estimated by the function :
V= 10,000e°05
Where V is the value of the asset in dollars and t is the age in years .Then the instantaneous
rate of change in the value of the asset, when the asset is 10 years old , is expected to be
about:
"Given the function : T(x) = (x+4)e"*. Answer questions 14 and 15.
14. Find f(-1).
a, -6e° b. 17? c 21e3 (« -21e3
15. Determine x so that f’(x) = 0.
a 5, -6/5 (0) 4,103 « 8,-2/3 d. 4,-
& 16.IF y=f(u)=u2+4u and u=g(x)= 1/x, then dy/dx at x= 1/2 will be:
(3% b. -64 c. 19/4 d, —51/2
uy
V. Evaluate: [a
Vv¥x+3
2
~ oo ( x +3)", (2 “f Lj
C
+a 7
a ) 7 {
t (de\eind ths ae sounded by: y= x? Ly
me LeeN'GIIUL UY Area DOUNGE Vi ysx -4, y=3x,and the x-axis swith x>0.
(Graph and shade the required region)
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LIBR ORY
OF HERUT
5. (12%)A woman has 12 friends,8 women and 4 men.
a) In how many ways can she invite 8 of them to dinner?
b) In how many ways can she invite Swomen and 4 men?