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PART 2 : RANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 11 questions.

Questions

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11 questions · timed · auto-graded

Question 13 Marks
Dhaval wishes to invest in a company. The following probability distribution is obtained for the past performance of this company in stock market :
Annual return on investment $(\%)$ $2$ $5$ $8$ $12$ $16$
Probability $0.2$ $0.25$ $0.3$ $0.15$ $0.1$
Dhaval wishes to invest in the company if the average annual rate of return is $10 \%$ or above. Will Dhaval invest in this company?
Answer
Average annual rate $=7.45 \%$
$\therefore$ Dhaval will not invest
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Question 23 Marks
The probability distribution of sale of strawberry boxes of a fruit vendor is as follows:
No. of boxes $20$ $21$ $22$ $23$ $24$ $25$
Probability $0.05$ $0.1$ $0.3$ $0.35$ $0.15$ $0.05$
Find mean and variance of the sale.
Answer
Mean $=22.6$, Variance $=1.34$
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Question 33 Marks
$10 \%$ customers among the customers of a bank enquire about loan. Among $6$ customers
arriving on a day, find the probability that
$(1)$ not a single customer enquires about loen.
$(2)$ more than one customers enquire about loan.
Answer
$(1)0.5314$, $(2) 0.1143$
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Question 43 Marks
$25 \%$ adults in a city are known to be diabetic. If $4$ persons are selected from this city, find the probability that at the most $2$ persons among them are diabetic.
Answer
$0.9493$
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Question 53 Marks
Generally $30 \%$ customers visiting an electronic store buy something. A sample of $5$ customers is selected every hour. In $30$ such samples, how many samples will have at least $2$ customers buying something ?
Answer
$14$
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Question 63 Marks
$70 \%$ persons among the residents of an area are vegetarian. Find the probability of having less than $4$ vegetarians in a sample of $5$ persons.
Answer
$0.4717$
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Question 73 Marks
If $n=9$ and $p(4)=2 p(5)$ for a binomial distribution, find the mean and variance of the distribution. $ 42 $
Answer
Mean $-3$. Variance $-2$
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Question 83 Marks
If the mean is $2$ and variance is $1.6$ of a binomial distribution, find its parameters. Comment on the skewness of the distribution.
Answer
$n=10, p=0.2$, Positive skewness
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Question 93 Marks
Find the value of constant $k$ in the following probability distribution. Also find the mean and variance of the variable. $ \begin{aligned} p(x) &=k, & & x=0,1,2,3,4 \\ &=0 . & & \text { Otherwise } \end{aligned} $
Answer
$k=\frac{1}{5}, \operatorname{Mean}-2$, Variance $=2$
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Question 103 Marks
In a game of selecting one card from a pack of cards, the player gets $₹ 13$ if a queen or jack card is selected. He gets $₹ 26$ for the selection of a king or ace and loses $₹ 13$ for any other card. Find the expected gain of the player.
Answer
$(1)\ \frac{1}{20}$,$(2)\ \frac{3}{4}$
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3 Marks Each - Statistics STD 12 Commerce Questions - Vidyadip