Tag: business mathematics and statistics

Quizzes (14) Questions (285)

Questions Related to business mathematics and statistics

Multiple choice business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

State whether the following statements are 'true' or 'false':
A sampling method that divides the population into homogeneous groups from which random samples are drawn is known as systematic sampling.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Dividing a population into homogeneous subgroups (strata) and drawing random samples from each is known as stratified random sampling, not systematic sampling. Therefore, the statement is false.

Multiple choice business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

State whether the following statements are 'true' or 'false':
In simple random sampling method, each unit of the population has an equal chance of being included in the sample.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple random sampling is defined by the property that every unit in the population has an equal probability of being selected.

Multiple choice business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

State whether the following statements are 'true' or 'false':
When properties of the units of the population have more dissimilarities, the use of stratified random sampling method is advantageous. 

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Stratified sampling is used to reduce variance when the population is heterogeneous by grouping similar units together.

Multiple choice business mathematics and statistics sampling methods population and sampling basic concepts of sampling sampling techniques and statistical inference

Population are unlimited in size are referred to as____________.

  1. infinite populations.

  2. finite populations.

  3. census method.

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Population refers to an entire set of people or objects present for the purpose of gathering data and when the population is unlimited in size i.e. it cannot be ascertained easily, it is known as infinite population.

Multiple choice business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

The demand function if $p = 60 + 2D - 10D^2$, the rate of charge in price with respect to demand is ______

  1. $\dfrac{60}{D} + 2 - 10D$
  2. $2 - 20D$
  3. $2 - 40D$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The rate of change of price with respect to demand is the derivative dp/dD. Differentiating p = 60 + 2D - 10D² term by term gives dp/dD = 0 + 2 - 20D = 2 - 20D. Option A incorrectly divides 60 by D, and Option C has an incorrect coefficient.

Multiple choice business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

Given the total cost function, $TC = a+bQ+cQ^2+dQ^3$, Find the Marginal cost.

  1. $b+2cQ+3dQ^2$
  2. $a + b+2cQ+3dQ^2$
  3. $a + 2b+2cQ+3dQ^2$

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have $TC=a+bQ+cQ^2+dQ^3$

$\Rightarrow$  $Marginal\,cost = \dfrac{d}{dQ}TC$

$\Rightarrow$  $Marginal\, cost=\dfrac{d}{dQ}(a+bQ+cQ^2+dQ^3)$

$\therefore$    $Marginal\,cost=b+2cQ+3dQ^2$

Multiple choice business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

 The total cost function is $TC = 12x + 2x^2$. Find the $MC$.

  1. $12-4x$
  2. $4x - 12$
  3. $12 + 4x$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$MC = \dfrac{\mathrm{d} TC}{\mathrm{d} x}$

$TC = 12x + 2x^{2}$
$\Rightarrow \dfrac{\mathrm{d} TC}{\mathrm{d} x}=12+4x$
$\Rightarrow MC = 12 + 4x$

Multiple choice business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

$y = 48x - 2x^2$
where, $y=$ Total revenue $ $ $.
$x = $ Output
At what output is total revenue a maximum?

  1. $2$
  2. $12$
  3. $48$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  We have given, $y=48x-2x^2$

$\Rightarrow$  Differentiate on both sides w.r.t $x$ we get,
$\Rightarrow$  $\dfrac{dy}{dx}=48-4x$          --- ( 1 )
$\Rightarrow$  Let $\dfrac{dy}{dx}=0$
$\Rightarrow$  $48-4x=0$
$\Rightarrow$  $4x=48$
$\Rightarrow$  $x=12$ is a turning point.
$\Rightarrow$  $\dfrac{d^2y}{dx^2}=-4$         [Differentiate ( 1 ) on both sides]
$\Rightarrow$  So, the turning point is a maximum 

Multiple choice business mathematics and statistics applications of calculus revenue functions from marginal revenue functions minimization of cost function and maximization of revenue function and profit function integral calculus – ii

The cost, in dollars, of producing $x$ gallons of detergent is given by
$C(x)=350+20x0.08x^2 + 0.0004x^3$
What is a formula for the marginal cost function $C'(x)$

  1. $C(x)=200.16x^2+0.0012x^2$
  2. $C(x)=200.16x+0.0012x^2$
  3. $C(x)=20x0.16x+0.0012x^2$
  4. $C(x)=20x0.16x^2+0.0012x^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$c'(x)=\cfrac{d}{dx}(c(x))$
$=2\times(100+0.8)x+3\times0.0004x^{2}$
$=200.16x+0.0012x^{2}$