Question Paper of Probability/Statistics/Proof

Question 1:

20+10+5+…. is a geometric series. Find which term of the series will be just

than 0.0001

Question 2:

$D u r i n g a b u s y c r i c k e t s e a s o n, D o n a l d i n c r e a s e d h i s b a t t i n g s c o r e b y 4 r u n s i n e a c h s u c c e s s i v e i n n i n g s . H e w a s d i s m i s s e d f o r 10 r u n s i n h i s f i r s t i n n i n g s o f t h e s e a s o n . (i) H o w m a n y r u n s d i d h e s c o r e i n h i s 15 t h i n n i n g s ? (i i) H o w m a n y i n n i n g s d i d i t t a k e f o r h i m t o s c o r e h i s f i r s t c e n t u r y o f t h e s e a s o n ? (N o r a : A c e n t u r y i s 100 r u n s .) (i i i) S h o w t h a t D o n a l d w i l l s c o r e a t o t a l o f 2 n^{2} + 8 n r u n s i n n i n n i n g s . (i v) H o w m a n y i n n i n g s w i l l i t t a k e D o n a l d t o p a s s 1000 r u n s f o r t h e s e a s o n ?$

Question 3:

$W h a t i s t h e v a l u e o f {\sum 2^{1 - r} ?}_{r = 4}^{4} (A) \frac{1}{64} (B) \frac{9}{8} (C) \frac{15}{8} (D) \frac{9}{4}$

Question 4:

$I n a g a m e, t w o p l a y e r s t a k e t u r n s a t d r a w i n g a n d t h e n i m m e d i a t e l y r e p l a c i n g a m a r b l e f r o m a b a g . T h e b a g c o n t a i n s 2 g r e e n a n d 3 r e d m a r b l e s . P l a y e r A d r a w s f i r s t . F o r A t o w i n h e m u s t d r a w a g r e e n m a r b l e . F o r B t o w i n h e m u s t d r a w a r e d m a r b l e . F i n d t h e p r o b a b i l i t y t h a t A w i n s o n h i s f i r s t d r a w . B w i n s o n h i s f i r s t d r a w . A w i n s i n f e w e r t h a n 4 o f h i s t u r n s . A w i n s e v e n t u a l l y .$

Question 5:

$t h e p o p u l a t i o n P o f a t o w n i s c h a n g i n g e x p o n e t a l l y P = P_{ο} e^{k t} . t i s t h e t i m e i n y e a r s . i) A t t h e s t a r t o f 2000 t h e p o p u l a t i o n w a s 15000 p e o p l e a n d a t t h e s t a r t o f 2010 i t w a s 35000 S h o w t h a t t h e g o w t h r a t e k i s a p p r o x i m e t l y 8.5 % . i i) U \sin g k = 0.085 a f t e h o w m a n y y e a r s t h e p o p u l a t i o n w i l l r e a s c h 50000 p e o p l e ?$

Question 6:

By using Simpson's rule with 5 function values, estimate the value of the integral $\int_{0}^{2} \log_{e} (x + 2) d x$

Question 7:

The personal assistance to the CEO of Spendupbig Retail chain start on an annual salary of $30,000 with an annual increase of $2,000.

Question 8:

Find his total earning after he has worked for the company for 15 years

Question 9:

In which year will his salary be $42,000

Question 10:

Find the value of the smallest term of the geometric series 4+10+25…. that is greater than $10^{20}$ .Write your answer in scientific notation correct to 3 significant figures.