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AGN108: Introductory Mathematics and Statistics for Agriculture (Quiz 2)

Department of Agric Engineering, UCC

This Quiz is a learning tool for the Introductory Mathematics and Statistics for Agriculture course. Select ONE correct answer for each of the 17 multiple choice questions in the Quiz.

After you have selected an answer option for a Question, click on the "Next" button to reveal the correct answer with its accompanying explanation. Thank you & Happy Learning!

Dr Ernest Ekow Abano, MGSAE, MASABE

Department of Agric Engineering, UCC

This Quiz is a learning tool for the Introductory Mathematics and Statistics for Agriculture course. Select ONE correct answer for each of the 17 multiple choice questions in the Quiz.

After you have selected an answer option for a Question, click on the "Next" button to reveal the correct answer with its accompanying explanation. Thank you & Happy Learning!

Dr Ernest Ekow Abano, MGSAE, MASABE

Samples of emissions from three suppliers are classified for conformance to air quality specifications. The results from 100 samples are summarized as follows:

		Conforms
		Yes	No
Supplier	1	22	8
Supplier	2	25	5
Supplier	3	30	10

Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample conforms to specifications. If a sample is selected at random, use the information to answer the following Question

What is the probability of (A ∪ B)?

A. 0.30

B. 0.70

C. 0.77

D. 0.85

E. 0.92

CORRECT ANSWER & EXPLANATION

		Conforms
			B
			Yes	No
Supplier	1	A	22	8
Supplier	2		25	5
Supplier	3		30	10

(A ∪ B) is all the elements in the shaded area, thus

(A ∪ B) = 8 + 22 + 25 + 30 = 85

Probability of (A ∪ B) = ⁸⁵/₁₀₀ = 0.85

Hence, the correct answer is D

CORRECT ANSWER & EXPLANATION

		Conforms
			B
			Yes	No
Supplier	1	A	22	8
Supplier	2		25	5
Supplier	3		30	10

(A ∪ B) is all the elements in the shaded area, thus

(A ∪ B) = 8 + 22 + 25 + 30 = 85

Probability of (A ∪ B) = ⁸⁵/₁₀₀ = 0.85

Hence, the correct answer is D

Samples of emissions from three suppliers are classified for conformance to air quality specifications. The results from 100 samples are summarized as follows:

		Conforms
		Yes	No
Supplier	1	22	8
Supplier	2	25	5
Supplier	3	30	10

What is the probability of (A^I ∪ B)?

A. 0.22

B. 0.70

C. 0.77

D. 0.85

E. 0.92

CORRECT ANSWER & EXPLANATION

		Conforms
			B
			Yes	No
Supplier	1	A	22	8
Supplier	2		25	5
Supplier	3		30	10

A’s compliment is both supplier 2 and 3, while B is the shaded portion under column B. The union represents the addition of both sets, hence

The correct answer is E

CORRECT ANSWER & EXPLANATION

		Conforms
			B
			Yes	No
Supplier	1	A	22	8
Supplier	2		25	5
Supplier	3		30	10

A’s compliment is both supplier 2 and 3, while B is the shaded portion under column B. The union represents the addition of both sets, hence

The correct answer is E

Samples of emissions from three suppliers are classified for conformance to air quality specifications. The results from 100 samples are summarized as follows:

		Conforms
		Yes	No
Supplier	1	22	8
Supplier	2	25	5
Supplier	3	30	10

What is the probability of (A ∩ B)?

A. 0.22

B. 0.70

C. 0.77

D. 0.85

E. 0.92

CORRECT ANSWER & EXPLANATION

		Conforms
			B
			Yes	No
Supplier	1	A	22	8
Supplier	2		25	5
Supplier	3		30	10

A intersection B is where the A shaded area intersect with the B shaded area.

This can be seen to 22

That Probability is therefore ²²/₁₀₀ = 0.22

Hence, the correct answer is A

CORRECT ANSWER & EXPLANATION

		Conforms
			B
			Yes	No
Supplier	1	A	22	8
Supplier	2		25	5
Supplier	3		30	10

A intersection B is where the A shaded area intersect with the B shaded area.

This can be seen to 22

That Probability is therefore ²²/₁₀₀ = 0.22

Hence, the correct answer is A

CORRECT ANSWER & EXPLANATION

The correct answer is therefore B

CORRECT ANSWER & EXPLANATION

The correct answer is therefore B

A. 1 min

B. 3 min

C. 4 min

D. 5 min

E. 6 min

CORRECT ANSWER & EXPLANATION

The correct answer is therefore A

CORRECT ANSWER & EXPLANATION

The correct answer is therefore A

On Monday, Oguaa hall volleyball team will play Casely Hayford hall. On Wednesday, Casely Hayford will play the team from Atlantic hall. On Friday, Atlantic hall will play Oguaa hall. In each game, either team has a 50 percent chance of winning.

What is the probability that Oguaa will win both its games?

A. ¹/₂

B. ³/₄

C. ¹/₄

D. ¹/₈

E. ¹/₁₆

CORRECT ANSWER & EXPLANATION

On Monday, Oguaa hall volleyball team will play Casely Hayford hall.

On Wednesday, Casely Hayford will play the team from Atlantic hall.

On Friday, Atlantic hall will play Oguaa hall.

In each game, either team has a 50% chance of winning., making A the correct answer

CORRECT ANSWER & EXPLANATION

On Monday, Oguaa hall volleyball team will play Casely Hayford hall.

On Wednesday, Casely Hayford will play the team from Atlantic hall.

On Friday, Atlantic hall will play Oguaa hall.

In each game, either team has a 50% chance of winning., making A the correct answer

What is the probability that Casely Hayford will lose its games?

A. ¹/₂

B. ³/₄

C. ¹/₄

D. ¹/₈

E. ¹/₁₆

CORRECT ANSWER & EXPLANATION

Given that each team has 50% chances of winning, it means also that, each team has 100-50% chance of losing.

Therefore, the probability that Casely Hayford team will lose its games is 50% or ¹/₂

The correct answer is therefore A

CORRECT ANSWER & EXPLANATION

Given that each team has 50% chances of winning, it means also that, each team has 100-50% chance of losing.

Therefore, the probability that Casely Hayford team will lose its games is 50% or ¹/₂

The correct answer is therefore A

What is the probability that Oguaa will win both its games and Casely Hayford will lose both its games?

A. ¹/₂

B. ³/₄

C. ¹/₄

D. ¹/₈

E. ¹/₁₆

CORRECT ANSWER & EXPLANATION

The correct option here is D

CORRECT ANSWER & EXPLANATION

The correct option here is D

A. ¹/₂

B. ³/₄

C. ¹/₄

D. ¹/₈

E. ¹/₁₆

CORRECT ANSWER & EXPLANATION

Therefore the correct answer is E.

CORRECT ANSWER & EXPLANATION

Therefore the correct answer is E.

CORRECT ANSWER & EXPLANATION

Option A is therefore the right answer

CORRECT ANSWER & EXPLANATION

Option A is therefore the right answer

The table below shows cable Internet subscribers in Town T by Region. If the four regions shown in the table are the only regions in Town T, the total of which two regions accounts for exactly 70 percent of all cable Internet subscribers in Town T?

= 1,000 subscribers
Region M
Region N
Region O
Region P

A. Regions M and N

B. Regions M and O

C. Regions N and O

D. Regions N and P

E. Regions O and P

CORRECT ANSWER & EXPLANATION

The question is asking for two regions that make up or sum up to exactly 7 of the 1,000 subscribers.

In all, there are 10 of the 1,000 subscribers.

So we look for two regions who total sum of subscribers will be 7.

That is Regions M and N

The correct answer is therefore A

CORRECT ANSWER & EXPLANATION

The question is asking for two regions that make up or sum up to exactly 7 of the 1,000 subscribers.

In all, there are 10 of the 1,000 subscribers.

So we look for two regions who total sum of subscribers will be 7.

That is Regions M and N

The correct answer is therefore A

Which of the following shaded regions illustrates A' ?

CORRECT ANSWER & EXPLANATION

The compliment of a set A is the set of all possible outcomes in a sample space that are not in the event A itself.

So here, you identify the circle for the set A and shade the region outside the set A.

The correct answer is therefore B

CORRECT ANSWER & EXPLANATION

The compliment of a set A is the set of all possible outcomes in a sample space that are not in the event A itself.

So here, you identify the circle for the set A and shade the region outside the set A.

The correct answer is therefore B

Which of the following shaded regions illustrates (A ∩ B)' ∪ C ?

CORRECT ANSWER & EXPLANATION

Therefore, the correct answer is C

CORRECT ANSWER & EXPLANATION

Therefore, the correct answer is C

What kind of model was used for this experiment?

A. Linear

B. Logarithmic

C. Quadratic

D. First order Polynomial

E. Exponential

CORRECT ANSWER AND EXPLANATION

From the model, you can see that the highest power of x is 2, hence it a quadratic model or a second order polynomial.

The correct answer is therefore C

CORRECT ANSWER AND EXPLANATION

From the model, you can see that the highest power of x is 2, hence it a quadratic model or a second order polynomial.

The correct answer is therefore C

How many factors or independent variables were studied in this experiment?

A. 2

B. 3

C. 4

D. 5

E. 1

CORRECT ANSWER & EXPLANATION

From the model, you can see that there are three factors I.e. X₁, X₂ and X₃

Hence the correct answer is B.

CORRECT ANSWER & EXPLANATION

From the model, you can see that there are three factors I.e. X₁, X₂ and X₃

Hence the correct answer is B.

Which of the factors had the most significant main effect on drying time ?

A. Temperature

B. Air velocity

C. Sample thickness

D. Drying time

E. All of the above

The factor that had the most significant contribution can be determined from the coefficient values attached to each factor, and. The higher the value, the more the effect.

Therefore, the highest value is 217.5, which is attached to and represents the temperature of the drying air.

Therefore the right answer is A.

The factor that had the most significant contribution can be determined from the coefficient values attached to each factor, and. The higher the value, the more the effect.

Therefore, the highest value is 217.5, which is attached to and represents the temperature of the drying air.

Therefore the right answer is A.

An automobile manufacturer provides vehicles equipped with selected options. Each vehicle is ordered.

With or without an automatic transmission systems
With or without air-conditioning
With one of three choices of a stereo systems
With one of four exterior colours.

There are four choices of exterior colours: red, white, blue, or brown. And four choices of interior colour: red, black, blue or brown. However, with a red exterior, only a black or red interior can be chosen; with a white exterior, any interior colour can be chosen, with a blue exterior, only a black, red or blue interior colours can be chosen. With a brown exterior, only a brown interior can be chosen.

What is the number of possible outcomes in the sample space?

A. 24

B. 48

C. 192

D. 120

E. 132

There are 2 possibilities for with or without transmission system, meaning S=2

With air or no air condition has 2 possibilities making the sample space for this S = 2 x 2 = 4

After this, there are three choices of stereo systems, making the sample space S = 4 x 3 = 12

There are four exterior colours for the vehicle but this is dependent on the interior colours as well.

With a red exterior colour, two options (black or red interior) are possible, making the sample space for this as S = 12 x 2 = 24

With a white exterior any interior colour (red, black, blue or brown ) can be chosen. There are 4 interior colours, hence there are 4 possibilities, making the sample space as S = 12 x 4 = 48

With a blue exterior, only a black, red or blue colours can be chosen, thus, there are 3 possibilities, making the sample space for this option as S = 12 x 3 = 36.

With a brown exterior, only a brown interior can be chosen, hence the total sample space for this arrangement is S = 12 x 1 = 12.

Therefore, the total sample space S = 24 + 48 + 36 + 12 = 120

The correct option is D