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Statistics 3 Marks Each

Board Question Paper : August 2020 · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 8 questions.

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8 questions · timed · auto-graded

Question 13 Marks
There are one dozen mangoes in a box of which $3$ mangoes are rotien. $3$ mangoes are randomly selected from the box with replacement. If $X$ denotes the number of rotten mangoes in the selected mangoes, obtain the probability distribution of $X$ and heance find the expected value of the rotten mangoes in the selected mangoes.
Answer
$0.75$
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Question 23 Marks
The mean and variance of the binomial distribution are $2$ and $\frac{6}{5}$ respectively. Find $P(x \leq 1)$ for this binomial distribution.
Answer
$0.3369$
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Question 33 Marks
Two six faces balanced dice and thrown simultaneoulsy. If the sum of numbers on both the dice is more than $7$ then find the probability that both the dice show same numbers.
Answer
$\frac{1}{5}$
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Question 43 Marks
The probability that a teenager comming to a restaurant for dinner orders pizza is $0.63 .$ The probability of ordering cold drink is $0.54.$ The probability that the teenager orders at least one out of pizza and cold drink is $0.88 .$ Find the probability that the teenager coming for dinner on a certain day orders only one of the two items from pizza and cold drink. OR From the following information of Krina Company, calculate cash flow from operating activities:If $5 P(A)=3 P(B)=2 P(A \cup B)=\frac{3}{2}$ for the events $A$ and $B$ then find $P\left(A^{\prime} \cup B^{\prime}\right)$.
Answer
$0.59$ or $\frac{19}{20}$
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Question 53 Marks
Obtain the linear equation for trend for a time series with $n=6, \sum y=501, \sum t y=1762$.
Answer
self practice
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Question 63 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 $(cm)$ Yicld of Maize $($Quintal per hectare$)$
Mean $30$ $500$
variance $25$ $10,000$
Correlation coefficient $= 0.80$
Estimate the yield of maize when the rainfall is $70\ cm$.OR Obtain the regression line of $Y$ on $X$ from the following data and estimate $Y$ for $X=30 . n=10, \sum x=250, \sum y=300, \sum x y=7900, \sum x^2=6500$
Answer
$\hat{y}=185 or \hat{y}=38$
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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$)$ $8$ $18$ $14$ $45$ $57$
Rate of growth $($per thousand$)$ $5$ $15$ $10$ $20$ $13$
Correlation coefficient $= 0.80$      
Answer
$r=0.7$
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Question 83 Marks
Compute the general index number using the following data and interprete it :
Items $A$ $B$ $C$ $D$ $E$ $F$
Wight $15$ $23$ $15$ $25$ $10$ $12$
Index No. $220$ $225$ $190$ $215$ $198$ $220$
Answer
$213.2$
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