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Statistics 3 Marks Each

Board Question Paper : July 2019 · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 10 questions.

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10 questions · timed · auto-graded

Question 13 Marks
The following measures are obtained to study the relation between rainfall in $cm .( X )$ and yield of Bajri in quintal per hectare $( Y )$ in ten different regions during monsoon :$n =10, \overline{ x }=40, \overline{ y }=175, S _{ x }=12, \operatorname{Cov}( x , y )=360$Obtain the regression. line of yield, $Y$ on rainfall $X$. Estimate the yield of Bajri when the rainfall $X$ is $30 cm$. E
Answer
$\hat{y}=150$
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Question 23 Marks
Person A speaks truth in $90 \%$ cases whereas Person $B$ speaks truth in $80 \%$ cases. Find the probability that person $A$ and $B$ differ in stating the same fact. One number is randomly selected from the natural number $1$ to $100 .$ If the selected number is a single digit number find the probability that it is a perfect square.
Answer
$\frac{2}{10}, 0.26$
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Question 33 Marks
In a game of hitting a target, the probability that Ramesh will fail in hitting the target is $2 / 5$. If he is given $3$ trials to hit the target, find the probability of the event he hits the target successfully in $2$ trials. State mean of this distribution.
Answer
$\frac{9}{5}$
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Question 43 Marks
The probability distribution of a random variable $X$ is as follow :
$X = x$ $0$ $1$ $2$ Total
$P(x)$ $\frac{1}{9}$ $\frac{4}{9}$ $\frac{4}{9}$ $1$
Answer
$\frac{4}{9}$
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Question 53 Marks
One number is randomly selected from the natural number $1$ to $100 .$ If the selected number is a single digit number find the probability that it is a perfect square.
Answer
$\frac{1}{3}$
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Question 63 Marks
Two balanced dice are thrown simultaneously. Find the probability that the sum of numbers on two dice is a multiple of $2$ or $3 .$
Answer
$\frac{2}{3}$
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Question 73 Marks
Obtain the linear equation for trend for a time series with $n=8, \Sigma y=344, \Sigma ty $=1342$
Answer
$65.06-4.9 t$
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Question 83 Marks
The following information is obtained to study the relationship between average rainfall $($in $cm.)$ and the yield of maize $($in quintal per hectare$)$ in different taluka of Gujarat :
Particulars Rainfall $(cm.)$
$(X)$		 Yield Of size $(Y)$
$($Quintal per hectare$)$
Mean $82$ $180$
Variance $64$ $225$
Correlation coefficient $r = 0-82$
Estimate the yield of maize when the rainfall is $60 \ cm.$
Answer
$a=53.72$
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Question 93 Marks
The information of health index $(x)$ and life expectancy $(y)$ is obtained for $10$ people. These data are ranked to find the rank correlation coefficient and the sum of squares of the ranks was found to be $42.5 .$ It was also observed that health index $70$ was repeated three times and life-expectancy $45$ was repeated twice in the data. Find the rank correlation coefficient using this information.
Answer
$r=0.73$
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Question 103 Marks
The index numbers of food and clothing among the different groups of cost of living are $150$ and $224.7$ respectively for the year $2015.$ The price of fuel has increased by $220 \%$. The expense on rent has increased from $₹ 4000$ to $₹ 6000$ and miscellaneous expenses increased by $1.75$ times. If the expenditure for the first four groups are $40 \%, 18 \%, 12 \%$ and $20 \%$ respectively, find the cost of living index number for the year $2015$ and interpret it.
Answer
$0.9635$
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3 Marks Each - Statistics STD 12 Commerce Questions - Vidyadip