Modular Assessment Grade 11: Statistics and Probability Mr. Antonio E. Soto JR

High School Unit
PAASCU Level III
Modular Assessment
Grade 11
Statistics and Probability
Mr. Antonio E. Soto Jr.
Name: _____________________________________ Date: __________________

Section: __________________________ Class No.: ______________
Part I. STATEMENT ANALYSIS

Determine whether each statement is TRUE or FALSE. Write your answer on the space
provided. (10 points)
_______________ 1. In a probability distribution, the probability of each event in the

sample space is less than or equal to 1.
_______________ 2. The number of cups of coffee a cafeteria serves each day is an

example of a discrete variable.
_______________ 3. Surveying 12 people who just watched a movie to give their

personal opinion or review of the film as an outcome of the
experiment satisfies the requirements of a binomial experiment.
_______________ 4. A coin is tossed. If a head occurs, then you gain 1 peso and if a tail
occurs, then you gain nothing. The theoretical average gain in
tossing the coin is 50 centavos.
_______________ 5. The total area under the normal distribution curve is less than 1.
_______________ 6. The data values in a normal distribution curve is less on the area to
the right of 4 standard deviations away on the right side of the
mean as compared to the area between 2 standard deviations from
the left and right side of the mean.
_______________ 7. The z score is the number of standard deviations that a

particular x value is away from the mean.
_______________ 8. The central limit theorem tells us that if the sample size is large
enough, the shape of the distribution of sample means approaches
a normal distribution.
_______________ 9. Given the scores in a sample data set, when the sample standard
deviation is calculated, all scores in the sample data set are used.
_______________ 10. The positive square root of a variance is called the absolute value.
1
Part II. NUMERICAL ANALYSIS
Perform the indicated operation and simplify. Show your complete solutions.
1. The percentage of couples where both parties are in the labor force is 62%. If 10 couples
are selected at random. Find the probability that at most 5 of the couples are working.
(3 points)
2. The average number of phone inquiries each week at a poison control center is 80. Find
the probability that it will receive at least 10 calls in a single day? (3 points)
3. Find the area under the standard normal distribution curve . (2 points)
a. Between z = − 1.24 and z = 0.63.
b. Sum of the areas to the left of z = − 0.75 and to the right of z = 2.38.
4. Find the z value that corresponds to the given area under the standard normal distribution
curve. (1 point)
0.4219
0 z
5. In a standard normal distribution, if P(− a < z < a) = 0.6083, find a. (1 point)
2
Part III. PROBLEM SOLVING
Perform the indicated operation and simplify. Show your complete solutions.
1. Information from the Department of Motor Vehicles indicates that the average age of
licensed drivers is 38.6 years with a standard deviation of 10.4 years. Assume that the
distribution of the driver’s ages is normal.
a. What proportion of licensed drivers are from 25 to 45 years old? (2 points)
b. Determine the ages of licensed drivers separating the upper 10% and lower 10%
percent of the population. (3 points)
2. Weights of newborn babies in a particular city are normally distributed with a mean of
3380 g and a standard deviation of 475 g.
a. A newborn weighing less than 2100 g is considered to be at risk, because the
mortality rate for this group is very low. If a hospital in the city has 500 births in a
year, how many of those babies are in the “at-risk” category? (3 points)
b. If we redefine a baby to be at risk if his or her birth weight is in the lowest 3%,
find the weight that becomes the cutoff separating at-risk babies from those who
are not at risk. (2 points)
c. If 20 newborn babies are randomly selected as a sample in a study, find the

probability that their mean weight is between 3200 g and 3500 g. (3 points)
3
3. Over the past 30 games between team A and team B, team A has won 14 times, team B
has won 11 times and the game has ended in a draw 5 times. If these two teams played 9
games this season, what is the probability that team 𝐴 would win 5 games, team 𝐵 would
win 3 games, and the remaining game would be a draw? (3 points)
4. The formula for the standard error (standard deviation of the distribution of sample
means) implies that as the sample size (n) increases, the size of the standard error
decreases. Explain the role of the standard error in comparing the sample mean and the
population mean. Use the definitions and concepts on sample means distribution and
standard error and show examples comparing the sample mean and the population mean
of a distribution when the standard error changes in value to express your answer.
(4 points)
Theme for SY 2020-2021: Called by Christ to witness, to serve, and to share.

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High School Unit

PAASCU Level III

Name: ___________________ Date:

Part I. STATEMENT ANALYSIS

_______________ 1. In a probability distribution, the probability of each event in the

_______________ 2. The number of cups of coffee a cafeteria serves each day is an

_______________ 3. Surveying 12 people who just watched a movie to give their

_______________ 7. The z score is the number of standard deviations that a

5. In a standard normal distribution, if P(− a < z < a) = 0.6083, find a. (1 point)

c. If 20 newborn babies are randomly selected as a sample in a study, find the

Theme for SY 2020-2021: Called by Christ to witness, to serve, and to share.

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