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WorksheetsProbability and Statistics Quiz
Total questions: 50
Worksheet time: 25mins
What do you call the ratio of the number of favorable outcomes to the number of possible outcomes?
Statistics
Probability
Sampling
Random Variable
What term is used to describe a collection or a set of possible outcomes of a random experiment?
Probability
Experiment
Sample Point
Sample Space
Which term gives a particular numerical value for each of the outcomes in the sample space of a RANDOM or probability experiment?
independent variables
dependent variables
random variable
probability
Which type of random variable has values that can be counted?
Discrete random variables
Continuous random variables
Qualitative random variables
Nominal random variables
In tossing five coins simultaneously, what is the possible values of the random variable Y which is the number of tails?
Y = {1, 2, 3, 4, 5}
Y = {1, 2, 3, 4,}
Y = {0, 1, 2, 3, 4, 5}
Y = {0, 1, 2, 3, 4}
By examining the possible outcomes when rolling two dice, which option correctly represents all cases where the sum of the dots is greater than or equal to 11?
(5,6), (6,5), (6,6)
(4,6), (6,4) , (5,5), (5,6), (6,5), (6,6)
(5,5), (5,6), (6,5), (6,6)
(6,6)
“The outcomes (4,6), (6,4), (5,5), (5,6), (6,5), and (6,6) all have sums greater than or equal to 11.” Evaluate this statement.
Correct – All listed outcomes satisfy the condition.
Incorrect – (4,6) and (6,4) do not meet the condition.
Incorrect – (5,5) should not be included.
Incorrect – Only (6,6) is valid.
What function summarize the probability that a discrete random variable takes on a particular value?
probability mass function
cumulative density function
function
random mass function
PMF can be expressed in different forms, which of the following is NOT a form of Probability Mass Functions?
Equation Form
Decimal
Graph Form
Tabular Form
What do you call the mean of a random variable?
Expected Value
Mean
Variance
Standard Deviation
What is the symbol used to denoted mean?
σ
sd
m
µ
What do you call the spread of the distribution of the random variable X?
Mean
Expected Value
Variance
Random Variable
Which of the following is NOT true about a probability mass function of a discrete variable?
The probability mass function is never negative.
The sum of all probabilities will always be equal to 1.
A probability mass function describes the frequency of random variable over the sample space.
The graph of the probability mass function is called a histogram.
Which of the following is NOT true about probability mass function?
The formula is f(x) = P[ X=x]
0 < P(X) < 1
It describes the probability of a random variable which is equal to a certain value over the sample space.
P(X) = 1
Which of the following DOES not belong to the group?
expected value
mean
average
variance
What does the probability mass function represent in a raffle scenario?
The PMF shows the distribution of ticket prices in the raffle.
The PMF represents the probabilities of winning different prizes in the raffle.
The PMF represents the total number of tickets sold in the raffle.
The PMF indicates the average prize amount in the raffle.
A fair coin was tossed thrice. Given the PMF table below, what is the expected value or mean?
3/2
3
1/2
5
If the probability that an event happens is 0.53, what is the probability that the event will not happen?
-0.53
0
0.47
0.53
The probabilities that a player will get 6 to 10 questions correct on a trivia quiz are shown below. What is the mean of the possible correct response?
7.2
7.4
7.3
7.1
Given the table below: What is the missing probability?
5/27
6/27
7/27
8/27
The student council will sell 200 raffle tickets at ₱50 each.
Only 1 ticket wins ₱1,000, the rest win nothing.
If you buy 1 ticket, what is your expected gain or loss?
Steps to guide you:
- Find the chance of winning (out of 200 tickets).
- Multiply the chance by the prize (₱1,000).
- Subtract the ticket cost (₱50) to get the expected value.
gain 45 pesos
loss 45 pesos
gain 950 pesos
loss 50 pesos
What do you call to the probability distribution of the CONTINUOUS variable?
probability mass function
normal probability distribution
standard normal variables
random sampling
random sampling
Also known as Gaussian distribution, after the German mathematician Carl Gauss who first described it.
Normal Distribution
Empirical Rule
Normal Curve
Validating Empirical Rule
Is used often in statistics for forecasting final outcomes.
Normal Distribution
Empirical Rule
Normal Curve
Validating Empirical Rule
The changes of this value shift the graph of the normal curve to the right or to the left.
Mean
Variance
Standard Deviation
Mode
It determines the shape of the graph. (height and width of the curve).
Standard Deviation
Mode
Mean
Variance
What is the shape of a normal distribution curve?
U-shaped
Zigzag
Bell-shaped
Skewed
What is the value of z-score if it lies BELOW the mean?
Positive
Negative
0
Same as the Mean
What is the value of z-score if it lies ABOVE the mean?
Positive
Negative
0
Same as the mean
When the standard deviation is low, what is the shape of the normal curve?
the normal curve is short and wide
the normal curve is skinnier and taller
the normal curve is denser in the left than to the center
the normal curve is denser in the middle than to the center
Which of the following is Mean, Median and Mode located at the Normal Curve?
Left
Right
Away the Curve
Center
Which of the following is the total area under the normal curve?
Less than 1
Greater than 1
Equal 1
Cannot be measured
Using the right z-table, what is the Area corresponds to z = 1.97
0.4757
0.4756
0.4755
0.4754
Using the right z-table, what is the Area corresponds to z = -1.05
0.3531
0.3532
0.3533
0.3534
Using the right z-table, what is the Area corresponds to z = 0.22
0.0869
0.0870
0.0871
0.0872
Using the right z-table, what is the Area corresponds to z = 3.12
0.4991
0.4992
0.4993
0.4994
A test score of 85 has a z-score of +1.5. What does this imply about the test’s mean and standard deviation?
The score is below the mean
The score is exactly equal to the mean
The score is 1.5 standard deviations above the mean
The standard deviation is 85
Two students took different standardized tests.
Student A scored 80 on a test with a mean of 60 and a standard deviation of 10. Student B scored 72 on a test with a mean of 60 and a standard deviation of 6. Which student performed better relative to their group?
Student A, because the raw score is higher
Student B, because the z-score is higher
Both performed equally well
Cannot be determined without sample size
What is the z-score corresponding to a normal score of 𝑋=70 in a set of scores assumed to be normally distributed with a mean of 50 and a standard deviation of 5?
2.0
3.0
4.0
5.0
What is the z-score corresponding to a normal score of 𝑋=65 in a set of scores assumed to be normally distributed with a mean of 25 and a standard deviation of 10?
2.5
3.0
4.0
1.5
What do you call to the entirety of the elements of a set of data?
population
sampling unit
sampling
samples
What do you call a sampling method that involves random selection?
non-probability sampling
probability sampling
convenience sampling
quota sampling
What do you call to the statistical process of selecting a predetermined sample from the population of interest?
population
sample
sampling unit
sampling
Which of the following is an example of sample?
The total number of students in a school.
The ages of all vendors in a public market
The Top-50 top-earning Filipino
The list of all countries in the world.
What is TRUE about the sample mean and the mean of the population?
they must be equal
they must be unequal
sample mean is bigger than mean of the population
sample mean and population mean are both under parameter
What is the use of statistic in relation to a population?
To describe the exact characteristics of the population
To provide a definitive value for the population parameter
To summarize the entire population data without sampling
To make inferences about the population from sample observations
What is the population mean of 1.23, 1.35, 2.56, 2.98, 3.01, 3.45, 4.67, 5.56, and 8.99? Use the population mean formula by finding the sum of the scores and dividing it by the total number of values.
3.76
3.98
4.12
4.23
What is the number of combinations of sample size 3 from a population consisting of 2, 4, 5, 7, 8, 10, 11, 14, 16? Use the Combination Formula
82
83
84
85
Suppose a researcher wants to survey every 5th household from a list of 500 households, but the first household is chosen randomly. Which sampling method is being used, and why is this approach advantageous compared to simple random sampling?
Cluster sampling, because it groups households into clusters
Stratified sampling, because it ensures representation from all subgroups
Systematic sampling, because it uses a random start and a fixed interval
Convenience sampling, because it selects easily accessible households
A statistician is comparing two approaches to estimating the mean of a population: one involves using a single sample, and the other involves calculating the distribution of the sample means from many repeated samples. Which approach provides more reliable insight into the variability of the population mean, and why?
Using a single sample, because it saves time and resources
Calculating the sampling distribution, because it shows how the statistic varies across multiple samples
Using a Poisson distribution, because it models rare events
Using a normal distribution, because population means are always normally distributed
