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Statistics 5 Mark Each

PART 2 : NORMAL DISTRIBUTION · Gujarat Board (GSEB) STD 12 Commerce (GSEB - English Medium). 6 questions.

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Question 15 Marks
The result of an examination is as follows:
Result No. of students
Pass with distinction $500$
Pass without distinction $3000$
Fail $1500$
Total $5000$
Minimum $40$ marks out of $100$ are necessary to pass this examination and at least $70$ marks are needed to get distinction. If the marks of examination follows normal distribution, find the mean and standard deviation of the distribution.
Answer
Mean $=48.72$, Standard deviation $=16.62$
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Question 25 Marks
$5 \%$ persons of a large group have heights less than $132 \ cm$ and $40 \%$ persons have height between $132 \ cm$ and $143 \ cm$. Assuming that the distributio of height of these persons is normal, find the mean and standard deviation of their height.
Answer
Mean $=48.72$, Standard deviation $=16.62$
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Question 35 Marks
The standard deviation of monthly salaries of a group of $150$ employees is $₹ 750 .$ The distribution of monthly salary is normal. If the probability of an employee having salary less than $₹ 11,125$ is $0.9332$, how many employees would have salary between $₹ 9,250$ and $₹ 11,500 ?$
Answer
Mean $=143.91$ inch, Standard deviation $=7.24$ inch
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Question 45 Marks
The average production of a certain grain in plots of one
acre in a taluka is $2000\ kg$ and the variance is $8100( kg )^2$. The production of grains follows normal distribution.
$(1)$ What is the minimum production in the $20 \%$ plots having maximum production ?
$(2)$ What percent of plots will have the production between $1950\ kg$ and $2150\ kg$ ?
Answer
$123$
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Question 55 Marks
The diameter of copper wire follows normal distribution.
If the mean of its normal distribution is $11\ mm$ and
standard deviation is $1\ mm$, find $P _{15}$ and 
$(D _9)$ of the distribution and interpret them.
Answer
$P_{15}=9.97 mm$, Diameter of wire will be less than
$9.97 mm$ in $15 \%$ of the cases $D_9=12.28\ mm$,
Diameter of wire will be less than $12.28\ mm$ in
$(90 \%)$ of the cases
$(1)\ 2075.6\ kg\ (2)\ 66.48 \%$
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Question 65 Marks
The average daily sale of tea at a tea stall is $800$ cups and
its standard deviation is $80$ cups. If the daily sale follows
normal distribution, how many days in a year will the sale
of tea be
$(1)$ more than $1000$ cups$?$
$(2)$ between $744$ and $856$ cups$?$
$(3)$ less than $660$ cups?
Answer
$(1)\ 2$ days $(2)\ 188$ days $(3)\ 15$ days
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5 Mark Each - Statistics STD 12 Commerce Questions - Vidyadip