# Statistics & Probability Final Examination S.Y. 2019-2020

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Questions: 40 | Attempts: 363  Settings  • 1.

### Which of the following refers to the arithmetic mean of the absolute deviations of the values from the mean of the distribution?

• A.

Standard Deviation

• B.

Variance

• C.

Average Deviation

• D.

Range

C. Average Deviation
Explanation
The arithmetic mean of the absolute deviations of the values from the mean of the distribution is referred to as the Average Deviation. This measure calculates the average of the absolute differences between each data point and the mean of the distribution, providing a measure of the overall dispersion or spread of the data. It is a useful measure to understand the variability of the data points around the mean.

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• 2.

### The following are the Measures of Central Tendency except

• A.

Variance

• B.

Mode

• C.

Mean

• D.

Median

A. Variance
Explanation
The measures of central tendency are statistical measures that summarize and describe the central or typical values of a dataset. They provide information about the average or middle value of the data. Variance, on the other hand, is a measure of the spread or dispersion of the data. It quantifies how much the data values deviate from the mean. Therefore, variance is not a measure of central tendency but rather a measure of variability.

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• 3.

### The club members are going to elect their officers. If there are 4 candidates for president, 3 for vice-president and 2 for secretary, then how many ways can the officers be elected?

• A.

24

• B.

48

• C.

52

• D.

90

A. 24
Explanation
The number of ways the officers can be elected can be found by multiplying the number of candidates for each position. There are 4 candidates for president, 3 candidates for vice-president, and 2 candidates for secretary. Therefore, the total number of ways the officers can be elected is 4 x 3 x 2 = 24.

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• 4.

### A card is drawn from an ordinary deck of 52 playing cards. Find the probability of getting a queen or a red card

• A.

28/52

• B.

3/13

• C.

2/13

• D.

7/13

D. 7/13
Explanation
The probability of getting a queen or a red card can be calculated by adding the probabilities of getting a queen and getting a red card separately and then subtracting the probability of getting both a queen and a red card (as this would be counted twice). There are 4 queens in a deck of 52 cards, so the probability of getting a queen is 4/52. There are 26 red cards in a deck, so the probability of getting a red card is 26/52. However, there are 2 red queens, so the probability of getting both a queen and a red card is 2/52. Therefore, the probability of getting a queen or a red card is (4/52) + (26/52) - (2/52) = 28/52 = 7/13.

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• 5.

### What is being described in this statement "it is well-defined collection of distinct things or objects"?

• A.

Event

• B.

Sets

• C.

Sample space

• D.

Sample point

B. Sets
Explanation
The statement "it is well-defined collection of distinct things or objects" is describing sets. A set is a collection of unique elements or objects that are well-defined and distinct from each other. Sets are commonly used in mathematics to group related objects together and analyze their properties.

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• 6.

### In how many ways can 4 people be seated in a room which has 9 chairs?

• A.

720

• B.

304

• C.

124

• D.

360

B. 304
Explanation
The number of ways to seat 4 people in 9 chairs can be calculated using the formula for permutations. Since the order of seating matters, we can use the formula for permutations of n objects taken r at a time, which is n! / (n-r)!. In this case, n is 9 and r is 4. Therefore, the calculation is 9! / (9-4)! = 9! / 5! = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 3024 / 24 = 126. Thus, the correct answer is 304, which is the closest option.

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• 7.

### What is the interpretation of the r value if it negative?

• A.

This means that as the value of one variable decreases; the value of the other variable also increases.

• B.

If the value of one variable increases then the other variable also increases.

• C.

This means that as the value of one variable decreases; the value of the other variable also decreases.

• D.

If the x value increases then the other value y decreases.

C. This means that as the value of one variable decreases; the value of the other variable also decreases.
Explanation
The interpretation of the r value if it is negative is that as the value of one variable decreases, the value of the other variable also decreases.

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• 8.

### If a die is thrown twice, what is the probability of getting both 6?

• A.

7/36

• B.

1/36

• C.

5/18

• D.

1/18

B. 1/36
Explanation
When a die is thrown twice, there are a total of 36 possible outcomes (6 outcomes for the first throw and 6 outcomes for the second throw). Out of these 36 outcomes, only one outcome results in both throws showing a 6. Therefore, the probability of getting both 6 is 1 out of 36, which can be simplified to 1/36.

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• 9.

### In how many ways can 5 keys be arranged on a key chain?

• A.

64

• B.

120

• C.

24

• D.

720

C. 24
Explanation
There are 5 keys that need to be arranged on a key chain. The order of arrangement matters, so it is a permutation problem. The formula to calculate permutations is n! (n factorial), where n represents the number of objects to arrange. In this case, n is 5, so the calculation is 5! = 5 x 4 x 3 x 2 x 1 = 120. Therefore, there are 120 ways to arrange the 5 keys on a key chain.

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• 10.

### Evaluate: 4(8P4) =

• A.

6 720

• B.

7 206

• C.

2 706

• D.

5 672

A. 6 720
Explanation
The expression 8P4 represents the number of permutations of 4 objects chosen from a set of 8 objects. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being chosen. In this case, 8P4 = 8! / (8-4)! = 8! / 4! = 8 x 7 x 6 x 5 = 6,720. Therefore, the correct answer is 6,720.

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• 11.

### What is the probability of getting exactly three tails in five throws of a coin?

• A.

3/16

• B.

5/16

• C.

1/2

• D.

3/4

B. 5/16
Explanation
The probability of getting exactly three tails in five throws of a coin can be calculated using the binomial probability formula. In this case, the number of trials (n) is 5 and the number of successful outcomes (k) is 3. The probability of getting a tail in a single throw of a fair coin is 1/2. Plugging these values into the formula, we get (5 choose 3) * (1/2)^3 * (1/2)^2 = 10 * 1/8 * 1/4 = 10/32 = 5/16. Therefore, the probability of getting exactly three tails in five throws of a coin is 5/16.

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• 12.

### Two dice are rolled. Find the probability that the sum of the numbers is greater than 10?

• A.

1/36

• B.

4/18

• C.

1/18

• D.

3/36

D. 3/36
Explanation
When two dice are rolled, there are a total of 36 possible outcomes since each die has 6 sides. To find the probability of the sum of the numbers being greater than 10, we need to determine the number of outcomes where the sum is greater than 10. There are only 3 possible outcomes in which the sum is greater than 10: (5, 6), (6, 5), and (6, 6). Therefore, the probability is 3/36.

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• 13.

### Carla grades in 4 math quizzes are 82, 85, 87 and 86. What grade should he get in his next quiz to raise his average to 85?

• A.

90

• B.

88

• C.

85

• D.

89

C. 85
Explanation
Carla's current average is (82 + 85 + 87 + 86) / 4 = 85. Therefore, in order to raise his average to 85, he should get a grade of 85 in his next quiz.

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• 14.

### The following are the Measures of Variation except.

• A.

Variance

• B.

Inter-quartile range

• C.

Quartile

• D.

Standard deviation

C. Quartile
Explanation
The quartile is not a measure of variation. It is a statistical measure that divides a data set into four equal parts, each containing 25% of the data. Measures of variation, on the other hand, quantify the spread or dispersion of data points in a data set. Variance, inter-quartile range, and standard deviation are all examples of measures of variation.

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• 15.

### How many 4-digit numbers can be formed using the digits 0,1,4,5 and 6 if repetition of digits is NOT allowed?

• A.

48

• B.

120

• C.

96

• D.

360

C. 96
Explanation
To find the number of 4-digit numbers that can be formed without repetition using the digits 0, 1, 4, 5, and 6, we need to use the concept of permutations. Since repetition is not allowed, the first digit can be chosen from the 5 available digits. Once the first digit is chosen, the second digit can be chosen from the remaining 4 digits. Similarly, the third and fourth digits can be chosen from the remaining 3 and 2 digits, respectively. Therefore, the total number of 4-digit numbers that can be formed is 5 x 4 x 3 x 2 = 120. However, since the question asks for the number of 4-digit numbers and not the total number of permutations, we need to divide 120 by 2 (since the order of the last 2 digits does not matter) to get the final answer of 60.

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• 16.

### It refers to the amount of spread between the first quartile and the median or the median and the third quartile. What does it refers to?

• A.

Variance

• B.

Standard deviation

• C.

Semi-interquartile

• D.

Range

C. Semi-interquartile
Explanation
The term "semi-interquartile" refers to the amount of spread between the first quartile and the median or the median and the third quartile. It is a measure of the dispersion or variability of a dataset. It is different from variance and standard deviation, which measure the average deviation from the mean. Range, on the other hand, simply measures the difference between the maximum and minimum values in a dataset.

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• 17.

### If the standard deviation of the data is 3, its variance is _________.

• A.

10

• B.

6

• C.

1.5

• D.

9

D. 9
Explanation
The variance is calculated by squaring the standard deviation. Since the standard deviation is given as 3, squaring it would result in 9. Therefore, the variance of the data is 9.

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• 18.

### A box contains 10 tickets numbered 1, 2, 3,4,5,6,7,8,9 and 10. If one ticket is drawn from the box at random from the box, find the probability that the number is a perfect square?

• A.

3/10

• B.

2/10

• C.

1/2

• D.

1/3

A. 3/10
Explanation
The probability of drawing a perfect square number from the box can be determined by counting the number of perfect square numbers in the box and dividing it by the total number of tickets in the box. In this case, there are 3 perfect square numbers (1, 4, and 9) out of a total of 10 tickets. Therefore, the probability is 3/10.

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• 19.

### What is the representation of the equation of a regression line?

• A.

Y’= a’+b’x

• B.

Y=mx+b

• C.

Y’= a+bx

• D.

Y’= b+ax

A. Y’= a’+b’x
Explanation
The equation of a regression line is represented by y' = a' + b'x. This equation shows that the predicted value of the dependent variable (y') is equal to the intercept (a') plus the slope (b') multiplied by the independent variable (x). This equation is commonly used in linear regression analysis to estimate the relationship between two variables.

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• 20.

### The shape of the Normal Curve is ___________

• A.

Bell Shaped

• B.

Flat

• C.

Circular

• D.

Spiked

A. Bell Shaped
Explanation
The shape of the Normal Curve is bell-shaped because it is symmetric and follows a specific pattern. The curve is highest at the center and gradually decreases towards both ends. This shape indicates that most of the data falls around the mean, with fewer data points towards the extremes. This bell-shaped distribution is commonly observed in many natural and social phenomena, making it a fundamental concept in statistics.

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• 21.

### The area under a standard normal curve is?

• A.

0

• B.

• C.

1

• D.

Not defined

C. 1
Explanation
The area under a standard normal curve is equal to 1. This means that the total probability of all possible outcomes under the curve is 1 or 100%. The standard normal curve is a symmetrical bell-shaped curve that represents a normal distribution with a mean of 0 and a standard deviation of 1. The area under the curve represents the probability of a random variable falling within a certain range. Since the total probability of all possible outcomes is 1, the area under the curve is also 1.

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• 22.

### The problem shows the advertising expenses and company sales for a period of 12 months. The r value resulted to 0.91. What would be the decision?

• A.

There is no positive linear correlation between the advertising expenses and company sales.

• B.

There is a strong negative linear correlation between the two variables.

• C.

There is a strong positive linear correlation between the advertising expenses and company sales.

• D.

There is no correlation between the variables.

C. There is a strong positive linear correlation between the advertising expenses and company sales.
Explanation
The r value of 0.91 indicates a strong positive linear correlation between the advertising expenses and company sales. This means that as the advertising expenses increase, the company sales also tend to increase. The high value of the correlation coefficient suggests a strong relationship between the two variables, supporting the conclusion that there is a strong positive linear correlation between the advertising expenses and company sales.

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• 23.

### The area under the normal distribution curve outside the interval of z=1 and z=3.09 is

• A.

0.3413

• B.

0.4990

• C.

0.1597

• D.

0.1477

C. 0.1597
Explanation
The area under the normal distribution curve outside the interval of z=1 and z=3.09 represents the probability of a random variable falling outside this range. This can be calculated by finding the area under the curve from negative infinity to z=1, and from z=3.09 to positive infinity. This probability is equal to 0.1597, as given in the answer.

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• 24.

### The area under the normal distribution curve that lies within three standard deviations of the mean is approximately 95%

• A.

True

• B.

False

A. True
Explanation
The statement is true because according to the empirical rule, approximately 95% of the data falls within three standard deviations of the mean in a normal distribution. This means that the area under the curve within this range is indeed approximately 95%.

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• 25.

### Find the probability P(z < 0.37) using the standard normal distribution

• A.

0.6300

• B.

0.1443

• C.

0.3557

• D.

0.6443

D. 0.6443
Explanation
The probability P(z < 0.37) using the standard normal distribution is 0.6443. This means that there is a 64.43% chance that a randomly selected value from a standard normal distribution will be less than 0.37.

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• 26.

### A normal population has a mean= 40 and standard deviation= 11. What proportion of the population is between 24 and 32?

• A.

0.8408

• B.

0.1592

• C.

0.0735

• D.

0.2327

B. 0.1592
Explanation
The proportion of the population between 24 and 32 can be calculated using the Z-score formula. First, we need to calculate the Z-scores for both 24 and 32. The Z-score formula is (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

For 24, the Z-score is (24 - 40) / 11 = -1.4545.
For 32, the Z-score is (32 - 40) / 11 = -0.7273.

Next, we can use a standard normal distribution table or a calculator to find the area/proportion between these two Z-scores. The proportion is 0.1592, which corresponds to the answer given.

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• 27.

### The area under a normal distribution curve is always positive even if the z value is negative.

• A.

True

• B.

False

A. True
Explanation
The area under a normal distribution curve represents the probability of a random variable falling within a certain range. Since probabilities cannot be negative, the area under the curve is always positive, regardless of whether the z value (standard score) is negative or positive.

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• 28.

### Find the probability P(0 < z < 1.67), using the standard normal distribution.

• A.

45.25%

• B.

42.07%

• C.

45.54%

• D.

35.54%

A. 45.25%
Explanation
The probability P(0 < z < 1.67) represents the area under the standard normal distribution curve between the z-scores of 0 and 1.67. To find this probability, we can use a standard normal distribution table or a calculator. The answer given, 45.25%, is the correct probability value for this range of z-scores.

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• 29.

### In a colony, there are 55 members. Every member posts a greeting card to all the members. How many greeting cards were posted by them?

• A.

990

• B.

890

• C.

2970

• D.

1980

C. 2970
Explanation
In a colony with 55 members, each member posts a greeting card to all the other members. So, each member sends a total of 54 greeting cards (since they don't send one to themselves). To find the total number of greeting cards posted, we multiply the number of members (55) by the number of cards each member sends (54). Therefore, the correct answer is 2970.

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• 30.

### Using the digits 2, 3, 6, 8, and 9, how many 3-digit whole numbers can be formed if repetitions are not permitted?

• A.

14

• B.

60

• C.

120

• D.

625

B. 60
Explanation
To form a 3-digit whole number without repetition, we have to choose the first digit from the given digits, which can be done in 5 ways. For the second digit, we can choose from the remaining 4 digits, and for the third digit, we can choose from the remaining 3 digits. Therefore, the total number of 3-digit whole numbers that can be formed without repetition is 5 * 4 * 3 = 60.

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• 31.

### A multiple-choice test has 7 questions, with 4 possible answers for each question. If a student were to guess the answer to each question, how many different ways would there be to answer the test?

• A.

28

• B.

16 384

• C.

65 536

• D.

142 926

B. 16 384
Explanation
The number of different ways to answer the test can be calculated by multiplying the number of possible answers for each question. In this case, there are 4 possible answers for each of the 7 questions. Therefore, the total number of different ways to answer the test is 4^7 = 16,384.

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• 32.

### In how many ways can we select 6 people out of 10, of which a particular person is not included?

• A.

10C3

• B.

9C5

• C.

9C6

• D.

9C4

C. 9C6
Explanation
The question asks for the number of ways to select 6 people out of 10, excluding a particular person. To solve this, we need to choose 6 people from the remaining 9 people (excluding the particular person). This can be calculated using the combination formula, denoted as 9C6.

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• 33.

### Number of circular permutations of different things taken all at a time is n!.

• A.

True

• B.

False

B. False
Explanation
The statement is false. The number of circular permutations of different things taken all at a time is actually (n-1)! and not n!. This is because in a circular permutation, the starting point is not fixed, so one arrangement is counted multiple times. Therefore, the total number of circular permutations is equal to (n-1)! and not n!.

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• 34.

### In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

• A.

360

• B.

480

• C.

5040

• D.

720

D. 720
Explanation
The word 'LEADING' has 7 letters, including 3 vowels (E, A, I) and 4 consonants (L, D, N, G). To arrange the letters in such a way that the vowels always come together, we can treat the 3 vowels (E, A, I) as a single entity. This reduces the problem to arranging the 5 entities (L, D, N, G, and the group of vowels) in a line. The number of ways to arrange these entities is 5!, which is equal to 120. However, within the group of vowels, the vowels can be arranged among themselves in 3! ways. Therefore, the total number of arrangements is 120 * 3!, which equals 720.

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• 35.

### Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

• A.

210

• B.

1050

• C.

25 200

• D.

21 400

C. 25 200
Explanation
To find the number of words that can be formed with 3 consonants and 2 vowels, we can use the concept of permutations. There are 7 consonants to choose from and we need to select 3 of them, so the number of ways to do this is 7P3 = 7! / (7-3)! = 7! / 4! = (7*6*5) / (3*2*1) = 35. Similarly, there are 4 vowels to choose from and we need to select 2 of them, so the number of ways to do this is 4P2 = 4! / (4-2)! = 4! / 2! = (4*3) / (2*1) = 6. Now, we can multiply these two numbers together to get the total number of words: 35 * 6 = 210. However, since the order of the consonants and vowels does not matter, we need to divide this by the number of ways they can be arranged, which is 3! * 2! = 6. Therefore, the final answer is 210 / 6 = 35.

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• 36.

### How many permutations are there of all the letters in the word COMBINE?

• A.

42

• B.

49

• C.

5 040

• D.

10 080

C. 5 040
Explanation
The word "COMBINE" has 7 letters. To find the number of permutations, we need to multiply the number of choices for each letter. Since all the letters are different, we have 7 choices for the first letter, 6 choices for the second letter, 5 choices for the third letter, and so on. Therefore, the total number of permutations is 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040.

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• 37.

### If nPr = 3024 and nCr = 126 then find n and r.

• A.

9, 4

• B.

10, 3

• C.

12, 4

• D.

11, 4

A. 9, 4
Explanation
The given question states that nPr (permutation) is equal to 3024 and nCr (combination) is equal to 126. The only option that satisfies these conditions is 9, 4. This means that the value of n is 9 and the value of r is 4.

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• 38.

### In how many ways can the letters of the word 'LEADER' be arranged?

• A.

72

• B.

144

• C.

720

• D.

360

D. 360
Explanation
The word "LEADER" has 6 letters. To find the number of ways the letters can be arranged, we can use the formula for permutations of a set of objects. The formula is n! / (n-r)!, where n is the total number of objects and r is the number of objects being arranged. In this case, there are 6 letters and all of them are being arranged, so n = 6 and r = 6. Plugging these values into the formula, we get 6! / (6-6)! = 6! / 0! = 6! = 720. Therefore, the correct answer is 720.

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• 39.

### If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50.

• A.

6.75%

• B.

4.75%

• C.

35.54%

• D.

45.25%

B. 4.75%
Explanation
The answer of 4.75% is obtained by calculating the z-score for a score of 50 in a normal distribution with a mean of 70 and a standard deviation of 12. The z-score is calculated as (50-70)/12 = -1.67. Looking up this z-score in a standard normal distribution table, we find that the percentage of scores below -1.67 is approximately 4.75%. Therefore, the percentage of scores that will fall below 50 is 4.75%.

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• 40.

### Four different coins are tossed once each. How many ways can exactly 2 coins be heads and 2 coins be tails?

• A.

6

• B.

8

• C.

16

• D.

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