3 Marks Each

Question 13 Marks

The probability that a person living in a city is a non-vegetarian is $0.20 $. Find the probability of at the most two persons out of $6$ persons randomly selected from the city is non-vegetarian.

Answer

$0.9011$

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Question 23 Marks

The probability distribution of the monthly demand of laptop in a store is as follows:

Demand of laptop	$1$	$2$	$3$	$4$	$5$	$6$
Probability	$0.10$	$0.15$	$0.20$	$0.25$	$0.18$	$0.12$

Answer

$2.22$

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Question 33 Marks

If $P ( A )=\frac{2}{3}, P ( B )=\frac{3}{5}, P ( B / A )=\frac{3}{4}$ for two events in the sample space of a random experiment, then find $P ( A / B )$.

Answer

$P(B / A)=\frac{1}{2} ; P(B / A)=\frac{5}{6}$

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Question 43 Marks

One number is randomly selected from the natural number $1$ to $100 . $ Find the probability that the number selected is either a single digit number or a perfect square.OR Two cities $A$ and $B$ of different states have rains on $60 \%$ and $75 \%$ days respectively during the monsoon. For the cities $A$ and $B$, find the probability on a certain monsoon day $:(1)$ both the cities have rains,$(2)$ at least one city has rains.Note : The events of rains on a day in these two cities are independent.

Answer

$\frac{9}{100}+\frac{10}{100}-\frac{3}{100}=\frac{16}{100}=\frac{4}{25}$ OR $0.16$ OR $(1)=\frac{9}{20} \text { OR } 0.18 \text { (2) } \frac{9}{10}=0.9$

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Question 53 Marks

Fit a linear equation from the following data for variable $(y)$ of a time series: $n =5, \Sigma y =190, \Sigma$ ty $=602$.

Answer

$\hat{y}=28.4+3.2 t$

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Question 63 Marks

The following results are obtained from the information of average rain and yield of a crop per acre in the last $10$ years of an arid region :

Particulars	Rainfall $(cm)$	Yield of crop $(Kg.)$
Mean	$18$	$970$
standard deviations	$2$	$38$
Correlation co-efficient $=0.6$

Answer

$₹ 33.58$ thousands or $₹ 33580 \hat{y}=1015.6$

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Question 73 Marks

The following information is obtained by a survey conducted by a town planning committee of a state.

city	$A$	$B$	$C$	$D$	$E$
Population (lakh)	$57$	$45$	$14$	$18$	$8$
Rate of growth (per thousand)	$13$	$20$	$10$	$15$	$5$

Find the rank correlation co-efficient between the population of the cities and the rate of growth of the population.

Answer

$r=0.7$

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Question 83 Marks

Obtain the chain base index number from the fixed base index nuimbers given below with the year $2007-08$ a the base year for the wholesale prices of machines and equipments :

year	$2008-09$	$2009-10$	$2010-11$	$2011-12$	$2012-13$
Index number of machines and equipments	$117.4$	$118$	$121.3$	$125.1$	$128.4$

Answer

$117.4 ; 100.51 ; 102.8 ; 103.13 ; 102.64$

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Statistics 3 Marks Each

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