4 Marks Each

Question 14 Marks

A producer produces $x$ units at cost $200 x+15 x^2$. The demand function is $P =$ $1200-10 x$. Find the profit function and how many units should be produced for maximum profit.

Answer

$\frac{1}{2}$

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Question 24 Marks

Find the value of $\lim _{x \rightarrow-3} \frac{2 x^2+7 x+3}{3 x^2+8 x-3}$.

Answer

$(1)\ 409$ persons $(2)\ 11$ persons

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Question 34 Marks

The weight of randomly selected $500$ adult persons from a region of a city follows normal distribution. The average weight of these persons in $55 \ kg$ and its standard deviation is $7\ kg :(i)$ Estimate the number persons having weight between $41 \ kg$ to $62 \ kg. (ii)$ Estimate the percentage of persons having weight less than $41 \ kg$.

Answer

Mode $= 40,\mu=2000$

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Question 44 Marks

$(A)$ For a normal distribution, the first quartile and the mean deviation are $20$ and $24$ respectively. Obtain an estimate of the value of mode.
$(B)$ The monthly production of units in a factory is normally distributed with mean $u$ and standard deviation $\sigma$. The $Z$ scores corresponding to the production of $2400$ units and $1800$ units are $1$ and $-0.5$ respectively. Find its mean and standard deviation.

Answer

$\frac{-3 x^2+12 x+15}{\left(x^2+5\right)^2}$

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Statistics 4 Marks Each

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