BPSU – CEA EECE0513 – COMPETENCY 1

EE Department Assignment #5 – AY2020/21 – 1ST SEM

Name: ________________________________________________________ Yr/Sec: ________

COMPLEX NUMBERS, PROBABILITIES, and Date: ____________ SCORE: ______
STATISTICS
MULTIPLE CHOICE/PROBLEM SOLVING (3 points each)
RUBRICS
Item Category/Description Point

1 Correct answer with complete solution 3

Correct answer but with incomplete solution; Wrong

2 1
answer/no answer but able to form equation or formula

3 No solution; no answer; with answer but no solution at all 0

Part 1: TERMINOLOGIES
1. Branch of statistics which deals with findings of solution in the field of engineering, medicine, education and economics is classified as
A. economic statistics B. applied statistics C. mathematical statistics D. industry statistics
2. Branch of statistics which deals with development of particular statistical methods is classified as
A. industry statistics B. economic statistics C. applied statistics D. mathematical statistics
3. In measuring the probability of any certain event, the zero represents
A. impossible events B. possible events C. certain event D. sample event
4. In measuring the probability of any certain event, the one which is in the limit of probability represents
A. certain event B. sample event C. impossible events D. possible events
5. Probability of the events must lie in the limits of
A. one to two B. two to three C. one to two D. zero to one
6. If one chooses to use a statistical procedure that reflects unconventional norms for one`s field:
A. it is crucial to state in a report that this is being done.
B. it is unnecessary to show how this new and possibly unaccepted method of analysis is being used.
C. It is irrelevant to discuss how the procedure differs from more traditional methods.
D. One should assume the reader will understand the implications this procedure has the conclusions drawn from the findings.
7. _____ is an example of a strategy used to reduce the likelihood of committing statistical error.
A. Filling in missing data B. Excluding outliers in analysis C. Altering or otherwise changing data D. Including outliers in analysis
8. Data analysis is defined as the:
A. process to ensure that research data, digital and traditional, is stored in a secure manner to ensure that procedural controls are in place
and adhered to in order to protect the integrity of data.
B. convention whereby research findings are prepared and disseminated to the scientific community.
C. process of gathering and measuring information on variables of interest, in an established systematic fashion that enables one to answer
stated research questions, test hypotheses, and evaluate outcomes.
D. the process of systematically applying statistical and/or logical techniques to describe and illustrate, condense, recap, and evaluate data.
9. The chief aim of analysis is to distinguish between:
A. an event occurring as either reflecting a true effect versus a one occurring by chance. C. quality control and quality assurance.
B. right from wrong. D. misrepresentation and plagiarism.
10. A common practice among investigators is to defer the selection of statistical analytic procedures to:
A. Statisticians B. Graduate assistants C. Defense committees D. Funding agency
11. The data which have already been collected by someone are called:
A. Raw data B. Array data C. Secondary data D. Fictitious data
12. Questionnaire survey method is used to collect which of the following?
A. Secondary data B. Qualitative variable C. Primary data D. None of these
13. Primary data and _____ data are the same.
A. grouped B. secondary C. ungrouped D. None of these
14. A parameter is a measure which is computed from _____.
A. population data B. sample data C. test statistics D. None of these
15. Which of the following measure of central tendency will always change if a single value in the data changes?
A. Mean B. Median C. Mode D. All of these
16. A complex number associated with a phase-shifted sine wave in polar form whose magnitude is in RMS and angle is equal to the angle of the
phase-shifted sine wave is known as:
A. Argand’s number B. Imaginary number C. Phasor D. Real number
17. √−1, √−5 are said to be
A. pure imaginary numbers B. non-imaginary numbers C. recurring decimal numbers D. finite numbers

Part 2: WORDED PROBLEMS

1. When the largest numerical value is 85, the smallest numerical value is 65, and the classes desired are 8, then the width of class interval is:
A. 18.75 B. 14.75 C. 13.75 D. 2.5
2. If the value of Σfx is 300, A= 35, number of observations are 15 and width of class interval is 5 then arithmetic mean is:
A. 135 B. 145 C. 150 D. 235
3. The mean of a distribution is 14 and the standard deviation is 5.What is the value of the coefficient of variation?
A. 60.4% B. 48.3% C. 35.7 % D. 27.8%

4. Mr. Jolly V. Hamburger raised all of his students' scores on a recent exam by 10 points. What effect did this have on the mean and median of
the scores?
A. The mean increased by 10 points, but the median remains the same
B. The median increased by 10 points, but the mean remains the same
C. The mean increased by 10 points, and the median increased by 10 points
D. The mean and the median remain the same
5. A store has five different lengths of extension cords for sale as shown in the table below. If the range of lengths of the five cords is 7 feet,
what is the greatest possible value of x?
Cord Length: 8 feet, 11 feet, 7 feet, 6 feet, x feet
A. 15 feet B. 18 feet C. 14 feet D. 13 feet
6. At a primate reserve, the mean age of all male primates is 15 years, and the mean age of all female primates is 19 years. Which of the
following must be true about the mean age m of the combined group of male and female primates at the primate reserve?
A. m = 17 B. m < 17 C. m > 17 D. 15 < m < 17
7. A total of 72 people participated in a survey about their music preferences. The results, separated by gender, are displayed below. According
to the survey, what is the probability that a male likes rap music?
Music Preference Male Female Total
Rock and Roll 8 8 16
Pop 14 13 27
Classical 5 8 13
Rap 4 6 10
Country and Western 2 2 4
Rhythm and blues 2 0 2
Total 35 37 72
A. 4 / 35 B. 5 / 36 C. 2 / 5 D. 2 / 3
8. Margo classified her favorite paintings hanging in a museum by both size and dominant color. The results are in the table below. Margo found
that 1/4 of her favorite large paintings were blue. How many of Margo's favorite paintings have red as the dominant color?
Dominant Color Large Small Total
Red ? 4 ?
Blue 5 ? ?
Total ? ? 24
A. 18 B. 19 C. 20 D. 21
9. The following equation represents the population growth of bacteria in a petri dish: P(t) = 350(2) t, where P(t) is the population after some
amount of time,t, measured in hours. Which of the following best describes the relationship between the population of bacteria, (t), and the
number of hours that have passed, t?
A. The relationship is linear since population has 350 more bacteria than the previous hour
B. The relationship is linear since population has 2 more bacteria than the previous hour
C. The relationship is exponential since the population is 350 times larger than the previous hour
D. The relationship is exponential since the population is 2 times larger than the previous hour
10. The table below classifies 103 elements as metal, metalloid, or nonmetal and as solid, liquid, or gas at standard temperature and pressure.
What fraction of all solids and liquids in the table are metalloids?
Solid Liquids Gas Total
Metals 77 1 0 78
Metalloids 7 0 0 7
Non-metals 6 1 11 18
Total 90 2 11 103
A. 7 / 77 B. 1 / 11 C. 7 / 92 D. 7 / 90
11. Five numbers are given: (5, 10, 15, 5, 15). Now, what would be the sum of deviations of individual data points from their mean?
A. 10 B. 25 C. 50 D. 0
12. A test is administered annually. The test has a mean score of 150 and a standard deviation of 20. If Rod’s z-score is 1.50, what was his score
on the test?
A. 180 B. 130 C. 30 D. 150
13. Consider the result of a fictional Stat 100 final exam taken by 120 students, as given in the following relative frequency distribution:
Grade Less than 50 50 - 59 60 - 69 70 - 79 80 - 89 90 - 100
Cumulative Frequency 15% 10% 30% 25% 15% 5%
How many students received at least a 70 on this exam?
A. 54 B. 45 C. 25 D. 30
14. Following are sample of ages (in months) of 18 children at a day care center: 36, 42, 18, 32, 22, 22, 25, 29, 30, 31, 19, 24, 35, 29, 26, 36, 24,
and 28. What is the standard deviation of the age of children?
A. 41.24 B. 11.33 C. 10.20 D. 6.42

15. The Vitamin C content of a particular brand of vitamin supplement pills is normally distributed with mean 490 mg and standard deviation 12
mg. What is the probability that a randomly selected pill contains at least 500 mg of Vitamin C?
A. 0.7967 B. 0.8333 C. 0.0525 D. 0.2033
16. The cholesterol content of large chicken eggs is normally distributed with a mean of 200 milligrams and standard deviation 15 milligrams. To
test if the claimed 200 mg value is reasonable, a sample of 60 large eggs is analyzed. Their average cholesterol content is 196 mg. What is
the P-value based on this sample?
A. 0.0197 B. 0.5239 C. 0.0524 D. 0.0317
17. The fine print on an instant lottery ticket claims that one in nine tickets win a prize. What is the approximate probability that you win more than
120 times if you purchase 900 tickets?
A. 0.5310 B. 0.2408 C. 0.0150 D. 0.0012
18. At a large university, the probability that a student takes calculus and statistics in the same semester is 0.0125. The probability that a student
takes statistics is 0.125. Find the probability that a student is taking calculus, given that he or she is taking statistics.
A. 0.1 B. 0.1125 C. 0.0016 D. 0.1375
19. A sample of 40 cows is drawn to estimate the mean weight of a large herd of cattle. If the standard deviation of the sample is 96 kg, what is
the maximum error in a 90% confidence interval estimate?
A. 25 kg B. 158 kg C. 58 kg D. 30 kg
20. If the standard deviation of x, y, z is p then the standard deviation of (3x + 5), (3y + 5), (3z + 5) is
A. 3p + 5 B. 3p C. p + 5 D. 9p + 15
21. In the complex number 3 + 4i, the absolute value is:
A. 10 B. 7.211 C. 5 D. 5.689
22. (6 cis 120°)(4 cis 30°) is equal to:
A. 10 cis 150° B. 24 cis 150° C. 10 cis 90° D. 24 cis 90°
23. Divide ((4 + 3i)/(2 – i)).
A. ((11 + 10i)/5) B. 1 + 2i C. ((5 + 2i)/5) D. 2 + 2i
24. Write –4 + 3i in polar form.
A. 5Լ36.87° B. 5Լ216.87° C. 5Լ323.13° D. 5Լ143.13°
25. Find the length of vector (2, 1,1).
A. √17 B. √21 C. √20 D. √19
1. 85-65 = 20. 1.So width would be 20÷8 =2.5.
3. CV= (SD÷ MEAN) ×100

= (5÷14)×100

CV = 35.71

10.

There are 7 metalloids that are solid or liquid, and there are 92 total solids and liquids. Therefore,

the fraction of solids and liquids that are metalloids is  .

11. First , find out the mean

Mean(X) =(5+10+15+5+15)/5
=50/5
=10
the sum of deviations of individual data points from their mean
=(10-5)+(10-10)+(10-15)+(10-5)+(10-15)
=5+0+(-5)+5+(-5)
=5+0-5+5-5
=10

12. We know that,

X = μ + Zσ
where Z is Ravi's score on the test
Replacing the values, we get,
X = 150 + (1.50*20)
= 150 + 30
= 180
180 is the required answer.
15. p(x>=500) =
z score =(score - mean)/ s
z score = ( 500 - 490)/ 12
=0.8333
p(x>=500) = p(z> 0.83)  = 0.2033
21. (3^2+4^2)^1/2 = (25)^1/2 = 5
20. 3x+5,3y+5,3z+5=3p

19. maximum error = 1.645*sd/sqrt(n) =  1.645*96/sqrt(40) = 24.96 

So correct answer is a) 25 kg

18. p(calculus|statistics) = p(calculus and statistics)/ p(statistics)

=0.0125/0.125
= 0.1
option A