The Rizal Memorial College, Inc.
Senior High School Unit
Purok Gulayan, Boizer Avenue, Brgy. Mankilam,
Tagum City, Davao del Norte
COR 10- PROBABILITY AND
STATISTICS
nd
2
Semester A.Y.: 2023-2024
MIDTERM EXAMINATION
1-2. Find the mean of the given
probability distribution.
A.13
X
P(X)
0
3
10
1
4
10
2
5
10
3
6
10
4
7
10
5
8
10
B. 12
C. 11
D. 10
distribution below find the value of
the mean.
A. 5.78
X
3
P(X)
0.3
4
0.27
5
0.50
6
0.10
7
0.10
B. 6.78
C. 7.78
D. 8.78
distribution below find the
value of the mean.
X
A. 6
1
P(X)
0.3
2
0.8
3
0.9
4
0.1
5
0.4
B. 7
C. 8
D. 9
7-8. Determine the value of K and
X
P(X)
compute for the
mean.
0
1
12
1
3
8
2
𝑘
3
1
6
4
1
8
1
a. 𝑘 = , 𝜇 = 1.875
4
c.
1
b. 𝑘 = , 𝜇 = 2.875
5
d.
1
𝑘 = , 𝜇 = 3.875
6
1
𝑘 = , 𝜇 = 4.875
7
9-10. Determine the variance and the
standard deviation of the given
probability distribution.
X
0
P(X)
0.04
1
0.38
2
0.11
3
0.07
4
0.4
a. 𝜎 2 = 3.04, 𝜎 = 1.43
b. b. 𝜎 2 = 4.04, 𝜎 = 1.34
c. 𝜎 2 = 2.04, 𝜎 = 1.43
d. 𝜎 2 = 5.04, 𝜎 = 4.13
For item 11-16. Refer to the
Probability Distribution Below.
X
P(X)
0
0.20
1
0.17
2
0.29
3
0.31
4
0.03
11-12. Compute the mean of the given
probability distribution above.
a. 𝜇 = 1.9
b. 𝜇 = 1.8
c. 𝜇 = 1.7
d. 𝜇 = 1.6
13-14. What is the variance of
the probability distribution?
a. 𝜎 = 1.17
b.𝜎 = 1.18
c. 𝜎 = 1.19
d.𝜎 = 1.20
15-16. What is the standard
deviation of the probability
distribution?
a. 𝜎 ≈ 1.09
2
2
c. 𝜎 ≈ 1.11
2
b.𝜎 ≈ 1.10
2
d.𝜎 ≈ 1.12
restaurant, Chef Diether gathered the
following information about similar
restaurants in the area: Using these
findings as probabilities for the new
restaurant’s profit how much can Chef
Diether expect to earn?
Percent
30%
P(X)
₱50,000 Loss
20%
0
10%
₱50,000 Profit
40%
₱150,000 Profit
a. ₱30,000
b. ₱40,000
c. ₱50,000
d. ₱60,000
19-20. What is the variance of
the given probability
distribution?
X
0
P(X)
0.61
a. 0.76
1
0.19
b. 0.96
2
0.11
c. 0.7996
0.09
d. 0.9776
3
21-22. Determine which score
below is an outlier of a normal
distribution with 𝝁 = 𝟏𝟒, d. 𝝈 = 𝟐. 𝟓
a. 9
c. 11.5
b.15
d.12.5
23-24. Which statement supports
the fact that a normal
distribution is symmetric about
its
mean?
a. Approximately 50% of data are less
than the mean, and approximately 50% of
the data are equal to the mean.
b. Approximately 75% of data are less
than the mean, and approximately 25% of
the data are greater than the mean.
c. Approximately 25% of data are less
than the mean, and approximately 75% of
the data are greater than the mean.
d. Approximately 50% of data are less
25-26. Given a set of scores with 𝝁 = 𝟐𝟎 and 𝝈 = 𝟒. 𝟓,
what is the score three standard deviations above
the mean?
a. 6.5
c. 33.5
b.11
d.29
27-28. What does the statement
“a normal curve is continuous”
imply?
a. It extends indefinitely to
the left.
b. It extends indefinitely to
the right.
c. It extends in indefinitely
in both directions.
d. it extends in both
29-30. Evaluate which scores below is an
outlier of a normal distribution with 𝝁 =
𝟓, 𝝈 = 𝟎. 𝟕𝟓
a.4.00
b.7.00
c. 6.00
d.5.80
31–32. If a dataset follows a normal
distribution with a mean of 50 and a
standard deviation of 10, what
percentage of the data lies between
30 and 70?
a. 34%
c. 95%
b. 68%
d. 99.7%
33–34. In a normally distributed data, what is the area of
the score that falls two standard deviations above the
mean in percent?
a. 2.28%
c. 2.30%
b. 2.29%
d. 2.31%
35–36. Which is the correct normal curve that
has an area of 0.28385?
a
.
c
.
b
.
d
.
37–38. Which of the following statements
about the normal curve is true?
I. It is a discrete distribution
II. It is characterized by a skewed shape
III. It is only applicable to small sample size
IV. It is also known as the Gaussian Distribution
a. I only
c. II only
b. II and III
d. IV only
39–40. In a normally
distributed data, what is the
area of the score that falls one
standard deviations below and
above the mean?
a.0.3171
c. 0.3173
b. 0.3172
d. 0.3174
41-45. Eliza’s gadget store was able
to sell the following number of
gadgets each day for 50 days. Solve
for the mean, variance, and standard
deviation.
Number of
gadgets sold
(G)
0
1
2
3
4
5
Number of
days
4
8
12
18
2
6
46-50. The average life span of
360 people is recorded to be
normally distributed with a mean
of 65 years and a standard
deviation of 3.06. About how many
people have a life span of
between 58.88 and 74.18 years?