ILOILO CITY NATIONAL HIGH SCHOOL
M.H. Del Pilar St., Molo, Iloilo City
Senior High School
Statistics and Probability
MIDTERM EXAMINATION
I.
Determine whether the following variables are discrete or continuous. Write D if it is discrete and C if it is continuous.
1. Travel time going to school.
2. Number of marriages last year
3. Total goals scored by the women’s hockey team
4. The speed of a bicycle
5. Age of employees in a certain company
6. Number of subjects offered and enrolled in per semester
7. Length of time of telephone call
8. Annual income of an individual
9. Yearly profit of a company
10. Number of employees in the company
II.
Identification
1. It is a sampling technique in which every nth member is taken from the population.
2. It is a form of probability distribution when all possible samples of size n are drawn repeatedly from the population.
3. It is the error used as an estimator of a population parameter.
4. It is used as estimator of a population parameter instead of the mean.
5. It is the square of standard deviation.
6. It is the sampling technique sometimes called area sampling because it is applied on a geographical basis.
7. It is the type of nonrandom sampling technique wherein a specified number of persons or certain types is included in the
sample.
8. It is the nonrandom sampling technique which is used for very small sample size.
9. It is a subset or small group selected from a population, either by random or nonrandom techniques.
10. It is a selection of n elements derived from population N which is the subject of the investigation in which each sample point
has an equal chance of being selected using proper sampling techniques.
III.
Choose the letter of your answer. Write “e” if the letter of your answer is not among the choices.
1. Which variable cannot take a value that is between one value and the next closest value?
a. Discrete
b. continuous
c. qualitative
d. undefined
2.
What do you call the table that shows the probability values of the outcomes of an experiment where the sum of probabilities is 1?
a. table of random numbers
c. frequency distribution table
b. probability distribution
d. probability table
3.
Which of the following is not a discrete variable?
a. pages of books
b. number of students
4.
5.
c. frequency of absences d. velocity of a bus
Which of the following is not a probability function of a probability distribution?
a. P(X=x): 0.1, 0.25, 0.15, 0.35, 0.15
b.
P (X=x): 20%, 50%, 15%, 15%
c.
P (X=x): , , ,
d.
P (X=x): , ,
2 1 2 1
4 4 4 4
2 2
4
,
2
7 7 14 14
About 90% of the applicants passes the admission test every year. How many of the 250 applicants are expected to pass the admission
test this year?
a.
6.
7.
8.
9.
200
b. 225
c. 120
d. 150
What do you call the set of possible values resulting from a random experiment?
a. Random variable
b. qualitative variable
c. quantitative variables
d. distribution table
What is the weighted average of all the possible values of random variables?
a. Mean
b. variance
c. standard deviation
d. range
What is the degree to which random value differ from the expected value?
a. Mean
b. variance
c. standard deviation
d. range
The square root of variance is called ____.
a. Mean
b. variance
d. range
c. standard deviation
10. Which of the following has only success or failure as the possible outcomes?
a. Joint Probability
b. Marginal Probability c. Binomial probability
d. Conditional probability
11. The distribution of data where the mean, median and mode are approximately equal and where the data is clustered closely around the
center is called the
a. Probability distribution
b. normal probability
c. central tendency
d. variability
1
Prepared by: DENZY MAE B. MATEO, Teacher III
12. What is the total area under the normal curve
a. 0.25
b. 0.5
c. 0.75
d. 1.0
13. Which of the following is not a property of a normal curve?
a. The curve is symmetric about zero.
b. The curve extends indefinitely in one direction.
c. The total area under the normal curve is equal to 100%.
d. The area can be determined based on the standard score or z-score.
For numbers 14-16: Danny is one of the students who took final examinations in 3 subjects. The result of their examination are as follows:
Subject
Math
English
Science
Average score of students (𝜇)
78
82
85
𝜎
5
9
15
Danny’s score (x)
85
87
92
14. In which subject did Danny get a higher score than the rest?
a. Math
b. English
c. Science
d. all subjects
15. In which subject did Danny get a lower score than the rest?
a. Math
b. English
c. Science
d. all subjects
16. If the top 7% of the examinees in Math will be given incentives, what must be their score to be part of the list?
a. 90 and higher
b. 95 and higher
c. 80 and higher
d. 85 and higher
17. What is the z-score of 𝑥 = 90 if 𝜇 = 95.3 and 𝜎 = 3?
a. 2.37
b. -2.55
c. -1.77
18. What is the area under the normal curve bounded by 𝑥 = 90 and 𝜇 = 95.3 if 𝜎 = 3?
a. 0.4616
b. 0.4608
c. -0.4616
d. 1.77
d. -0.4608
19. What is the probability that an amount between P85,000 to P110,000 will be randomly chosen if the mean is P100,000 with a standard
deviation of P15,000?
a. 58.99%
b. 34.13%
c. 24.86%
d. 11.12%
20. What is the probability that a randomly selected value lies between 115 to 125 if the mean is 100 with a standard deviation of 15?
a. 58.99%
b. 34.13%
c. 24.86%
d. 11.12%
IV.
Perform the following.
3(𝑥−2)2 +3
28
1.
Determine the area of the mass function 𝑓(𝑥) =
2.
The following random variables show the number of successful trials in joining competitions. Find the mean and standard deviation.
x
P(X=x)
(𝑥 − 𝜇)2
(𝑥 − 𝜇)2 ∙ 𝑃(𝑋 = 𝑥)
𝑥 ∙ 𝑃(𝑋 = 𝑥)
𝑥−𝜇
0
0.2
1
0.35
2
0.25
3
0.3
when 0 ≤ 𝑥 ≤ 4. Draw the figure.
𝜇=
𝜎2 =
𝜎=
3.
A couple plans to have children in the future. What is the probability of having exactly 3 boys out of 4 children?
4.
Find the area under the normal curve in percent of the following conditions:
a. From 𝑧 = 0 𝑡𝑜 𝑧 = 2.07
b. From 𝑧 = 0 𝑡𝑜 𝑧 = −1.03
c. From 𝑧 = −2.33 𝑡𝑜 𝑧 = 3.03
5.
Given the mean 𝜇 = 120 with a standard deviation of 25, find the area under the normal curve when x is:
a. From 100 to 200
b. From 80 to 110
c. Above 130
6.
The average net sales per year of the products in 60 branches of the DG Company is P85 million with a standard deviation of P15
million. Determine how many branches have a sales of:
a. P 60 million to 85 million
b. Above 110 million
7.
Solve for the sample size n by using the Sloven’s formula given the following values.
a. N = 12000 and 𝑒 = 5%
b. N = 30000 and 𝑒 = 10%
8.
Solve the problem: below:
De Guzman Co. claims that the average life of their battery products lasts for 26 hours with a standard deviation of 5 hours. What is
the probability that 35 random pieces of their batteries have average life span of less than 24.3 hours?
2
Prepared by: DENZY MAE B. MATEO, Teacher III