11th Business Maths Weekly Test - 1 ( Descriptive Statistics and Probability )

MABS Institution

11th Business Maths Weekly Test - 1 ( Descriptive Statistics and Probability )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Probability of an impossible event is

Harmonic mean is the reciprocal of

Median of the values.
Geometric mean of the values.
Arithmetic mean of the reciprocal of the values.
Quartiles of the values.

Median is same as

Q₁
Q₂
Q₃
D₂

The correct relationship among A.M.,G.M.and H.M.is:

A.M.
G.M.≥A.M.≥H.M.
H.M.≥G.M.≥A.M.
A.M.≥G.M.≥H.M.

The geometric mean of two numbers 8 and 18 shall be

12
13
15
11.08

When an observation in the data is zero, then its geometric mean is

Negative
Positive
Zero
Cannot be calculated

The two events A and B are mutually exclusive if

\(P\left( A\cap B \right) =0\)
\(P\left( A\cap B \right) =1\)
\(P\left( A\cup B \right) =0\)
\(P\left( AUB \right) =1\)

The median of 10,14,11,9,8,12,6 is

If two events A and B are dependent then the conditional probability of P(B/A) is

\(P(A)P(B/A)\)
\(\frac { P(A\cup B) }{ P(B) } \)
\(\frac { P(A\cap B) }{ P(A) } \)
\(P(A)P(A/B)\)

Let a sample space of an experiment be S = { E₁,E₂,....., En} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to

0
1
\(\frac { 1 }{ 2 } \)
\(\frac { 1 }{ 3 } \)

Part - B

Generic 2 - Answer All Question

A family has two children. What is the probability that both the children are girls given that at least one of them is a girl?

A bag contains 5 white and 3 black balls. Two balls are drawn at random one after the other without replacement. Find the probability that both balls drawn are black.

Find the first quartile and third quartile for the given observations
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have
(i) No woman (ii) One man (iii) No man

A person purchases tomatoes from each of the 4 places at the rate of 1kg., 2kg., 3kg., and 4kg. per rupee respectively .On the average, how many kilograms has he purchased per rupee?

Part - C

Generic 3 - Answer All Question

Calculate Harmonic Mean for the following data given below

Value 0-10 10-20 20-30 30-40 40-50

Frequency 8 12 20 6 4

Calculate the geometric mean of the data given below giving the number of families and the income per head of different classes of people in a village of Kancheepuram District.

Class of people No. of Families Income per head in 1990 (Rs)

Landlords 1 1000

Cultivators 50 80

Landless labourers 25 40

Money- lenders 2 750

School teachers 3 100

Shop-keepers 4 150

Carpenters 3 120

Weavers 5 60

Find Q₂ for 37, 32, 45, 36, 39, 37, 46, 57, 27, 34, 28, 30, 21
A and B are two events such that P(A)\(\neq \)0. find P(B/A) if (i) A is a subset of B (ii) \(A\cap B=\phi \)

Calculate the value of quartile deviation and its coefficient from the following data

Roll No. 1 2 3 4 5 6 7

Marks 20 28 40 12 30 15 50

Part - D

Generic 5 - Answer All Question

Find out the coefficient of mean deviation about median in the following series

Age in years 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of persons 8 12 16 20 37 25 19 13

Age in years	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80
No. of persons	8	12	16	20	37	25	19	13

There are 3 boxes containing respectively 1 white, 2 red, 3 black balls; 2 white, 3 red and 1 black ball; 2 white, 1 red, 3 black balls. A box is chosen t random and from it 2 balls are drawn at random. The 2 balls are 1 red and 1 white. What is the probability that they come from the second box?

A factory has 3 machines A₁, A₂, A₃ producing 1000, 2000, 3000 bolts per day respectively. A₁ produces 1% defectives, A₂ produces 1.5% and A₃ produces 2% defectives. A bolt is chosen at random and found defective. What is the probability that it comes from machine A₁?

In a shooting test the probability of hitting the target are \(\frac{3}{4}\) for A, \(\frac{1}{2}\) for B and \(\frac{2}{3}\) for C. If all of them fire at the same target, calculate the probabilities that
(i) All the three hit the target
(ii) Only one of them hits the target
(iii) At least one of them hits the target
Three coins are tossed simultaneously. Consider the events A ‘three heads or three tails’, B ‘atleast two heads’ and C ‘at most two heads’ of the pairs (A, B), (A, C) and (B, C), which are independent? Which are dependent?

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Class of people	No. of Families	Income per head in 1990 (Rs)
Landlords	1	1000
Cultivators	50	80
Landless labourers	25	40
Money- lenders	2	750
School teachers	3	100
Shop-keepers	4	150
Carpenters	3	120
Weavers	5	60

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11th Business Maths Weekly Test - 1 ( Descriptive Statistics and Probability )

MABS Institution

11th Business Maths Weekly Test - 1 ( Descriptive Statistics and Probability )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

Probability of an impossible event is

Harmonic mean is the reciprocal of

Median is same as

The correct relationship among A.M.,G.M.and H.M.is:

The geometric mean of two numbers 8 and 18 shall be

When an observation in the data is zero, then its geometric mean is

The two events A and B are mutually exclusive if

The median of 10,14,11,9,8,12,6 is

If two events A and B are dependent then the conditional probability of P(B/A) is

Let a sample space of an experiment be S = { E1,E2,....., En} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to

Part - B

Generic 2 - Answer All Question

A family has two children. What is the probability that both the children are girls given that at least one of them is a girl?

A bag contains 5 white and 3 black balls. Two balls are drawn at random one after the other without replacement. Find the probability that both balls drawn are black.

Find the first quartile and third quartile for the given observations 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have (i) No woman (ii) One man (iii) No man

A person purchases tomatoes from each of the 4 places at the rate of 1kg., 2kg., 3kg., and 4kg. per rupee respectively .On the average, how many kilograms has he purchased per rupee?

Part - C

Generic 3 - Answer All Question

Calculate Harmonic Mean for the following data given below Value 0-10 10-20 20-30 30-40 40-50 Frequency 8 12 20 6 4

Find Q2 for 37, 32, 45, 36, 39, 37, 46, 57, 27, 34, 28, 30, 21

A and B are two events such that P(A)\(\neq \)0. find P(B/A) if (i) A is a subset of B (ii) \(A\cap B=\phi \)

Calculate the value of quartile deviation and its coefficient from the following data Roll No. 1 2 3 4 5 6 7 Marks 20 28 40 12 30 15 50

Part - D

Generic 5 - Answer All Question

Find out the coefficient of mean deviation about median in the following series Age in years 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No. of persons 8 12 16 20 37 25 19 13

There are 3 boxes containing respectively 1 white, 2 red, 3 black balls; 2 white, 3 red and 1 black ball; 2 white, 1 red, 3 black balls. A box is chosen t random and from it 2 balls are drawn at random. The 2 balls are 1 red and 1 white. What is the probability that they come from the second box?

A factory has 3 machines A1, A2, A3 producing 1000, 2000, 3000 bolts per day respectively. A1 produces 1% defectives, A2 produces 1.5% and A3 produces 2% defectives. A bolt is chosen at random and found defective. What is the probability that it comes from machine A1?

Three coins are tossed simultaneously. Consider the events A ‘three heads or three tails’, B ‘atleast two heads’ and C ‘at most two heads’ of the pairs (A, B), (A, C) and (B, C), which are independent? Which are dependent?

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Let a sample space of an experiment be S = { E₁,E₂,....., En} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to

Find the first quartile and third quartile for the given observations
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have
(i) No woman (ii) One man (iii) No man

Calculate Harmonic Mean for the following data given below

Value 0-10 10-20 20-30 30-40 40-50

Frequency 8 12 20 6 4

Find Q₂ for 37, 32, 45, 36, 39, 37, 46, 57, 27, 34, 28, 30, 21

Calculate the value of quartile deviation and its coefficient from the following data

Roll No. 1 2 3 4 5 6 7

Marks 20 28 40 12 30 15 50

Find out the coefficient of mean deviation about median in the following series

Age in years 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of persons 8 12 16 20 37 25 19 13

A factory has 3 machines A₁, A₂, A₃ producing 1000, 2000, 3000 bolts per day respectively. A₁ produces 1% defectives, A₂ produces 1.5% and A₃ produces 2% defectives. A bolt is chosen at random and found defective. What is the probability that it comes from machine A₁?