3 Marks Each

Question 13 Marks

Following results are obtained for a bivariate data :

Particulars	$x$	$y$
No. of observations	$8$
Sum of squares of deviations taken from Mean	$130$	$145$
Sum of product of deviations taken from Mean	$115$
Mean	$100$	$100$

Obtain the regression line of $y$ on $x$.

Answer

$\hat{y}=12+0.88 x$

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Question 23 Marks

The information of price $($in $₹)$ of a pen and the supply of pen $($in units$),$ at the end of each month of a year for a company is given below. Estimate the supply of pen when its price is $₹ 40$.

Detail	Price $(x)$	Supply $(y)$
Average	$30$	$500$
variance	$25$	$10,000$
$r = 0.8$

Answer

$660$ units.

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Question 33 Marks

An official has ranked nine villages of a sample on the basis of the work done in the area of 'Swachchata Abhiyan' and 'Beti Bachao Ablliyan' by the villages. The ranks are as given below

Village	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$
Rank forSwachchata Abhiyan	$4$	$8$	$7$	$1$	$9$	$5$	$6$	$2$	$3$
Rank for Beti Bachao Abhiyan	$6$	$8$	$5$	$1$	$9$	$7$	$3$	$4$	$2$

Find Rank Correlation Coefficient between the performances of the villages In in two Abhiyans.

Answer

$r \cong 0.78$

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Question 43 Marks

The data about bi-monthly closing prices of shares of a company in the year $2020$ is given below. Compute the Chain base index number :

Month	January	March	May	July	September	November
price(₹)	$22$	$21.20$	$22$	$23$	$24.70$	$26$

Answer

$96.36 ; 103.77 ; 104.55 ; 107.39 ; 105.26$

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Question 53 Marks

If the demand function of pizza is $p=150-4 x$, then find the marginal revenue when demand is of $3$ pizzas.

Answer

$\frac{d R}{d x}=126$

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Question 63 Marks

A problem is given to $6$ students to solve. The probability of getting correct solution of the problem by any student is $0.6 .$ Students are trying to solve the problem independently. Find the probability of getting the correct solution by only $2$ out of $6$ students.

Answer

$0.1382$

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Question 73 Marks

During a war, on an average one ship out of $9$ got sunk in a certain Voyage. Find the probability that exactly $5$ out of a convoy of $6$ ships would arrive safely.

Answer

$0.37$

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Question 83 Marks

Two events $A$ and $B$ in the sample space of a random experiment are mutually exclusive. If $3 P ( A )=4 P ( B )=1$, then find $P ( A \cup B )$.

Answer

$\frac{7}{12}$

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Question 93 Marks

Four couples $($husband-wife$)$ attend a party. Two persons are randomly selected from these $8$ persons. Find the probability that the selected persons are $-(1)$ husband and wife $(2)$ one man and one woman $(3)$ one man and one woman who are not husband and wife.

Answer

$P ( C )=\frac{3}{7}$

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Question 103 Marks

Find the probability of getting $R$ in the first place and $M$ in the last place when all the letters of the word $\text{RANDOM}$ are arranged in all possible ways.

Answer

$\frac{1}{30} .$

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Question 113 Marks

Obtain the linear equation for trend for a Time Series with$n=8, \sum y=344, \quad \sum t y=1342 \text {. }$

Answer

$\hat{y}=65.05-4.9 t$

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Question 123 Marks

If the increase in the price relatives of three items is $250 \%, 265 \%$ and $300 \%$ respectively and if the ratio of the importance of these items is $8: 7: 5$, find the general price index number.

Answer

$367.75$

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Statistics 3 Marks Each

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