MATH 110 ALL MODULES (1,2,3,4,5,6,7,8,9,10) EXAM :
INTRODUCTION TO STATISTICS-PORTAGE LEARNING –
QUESTIONS AND ANSWERS | VERIFIED AND WELL DETAILED
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1. A researcher is analyzing the daily customer wait times at a local bank branch. The data
collected represents the time in minutes for 40 randomly selected customers. Which level of
measurement best describes this wait time data?
A. Nominal level
B. Ordinal level
C. Interval level
D. Ratio level
Ratio level data possesses all the properties of interval data, plus a true, non-arbitrary zero
point representing the complete absence of the characteristic. A wait time of zero minutes
means no wait at all, and ratios between values are meaningful (e.g., a 10-minute wait is twice
as long as a 5-minute wait).
2. A manufacturing plant tracks the defect rate of electronic components produced on
assembly line A versus assembly line B. The line supervisor computes the mean, median,
and mode for each line. If the distribution of defects on assembly line A has a long tail
extending toward higher defect counts, what is the most likely relationship between its
mean and median?
A. The mean is less than the median
B. The mean is equal to the median
C. The mean is greater than the median
D. There is no mathematical relationship between mean and median in skewed distributions
A distribution with a long tail extending toward higher values (positive skew) pulls the mean
in the direction of the tail, making it greater than the median because the mean is sensitive to
extreme values.
3. In a clinical trial for a new cholesterol-lowering medication, patient dropouts due to
adverse side effects are recorded. If a dataset of patient recovery times contains extreme
,outliers caused by underlying genetic anomalies in a few subjects, which measure of center
and spread is most appropriate to report?
A. Mean and standard deviation
B. Median and interquartile range
C. Mode and range
D. Variance and mean absolute deviation
The median and interquartile range are resistant statistics that are minimally affected by
extreme outliers, whereas the mean and standard deviation can be heavily skewed by extreme
data points.
4. An online retailer wants to estimate the average spending of shoppers during a holiday
sale event. They divide the customer database into tiers based on past purchasing history
(Bronze, Silver, Gold, Platinum) and randomly select a proportional number of customers
from each tier. What sampling technique is being utilized?
A. Simple random sampling
B. Systematic sampling
C. Stratified sampling
D. Cluster sampling
Stratified sampling involves dividing the population into homogeneous subgroups (strata)
based on specific characteristics and then drawing a random sample from each stratum to
ensure representation across all groups.
5. A diagnostic test for a rare pulmonary condition has a false positive rate of 5% and a
false negative rate of 2%. If the overall prevalence of the condition in the tested patient
population is 3%, what statistical theorem or rule is necessary to compute the probability
that a patient who tests positive actually has the condition?
A. The Central Limit Theorem
B. Bayes' Theorem
C. Chebyshev's Theorem
D. The Empirical Rule
, Bayes' Theorem provides a mathematical formula for calculating conditional probabilities,
specifically updating the probability of an event (having the condition) given new evidence (a
positive test result) and prior prevalence rates.
6. A quality control engineer measures the tensile strength of steel cables. The distribution
of strengths is approximately bell-shaped with a mean of 500 megapascals and a standard
deviation of 25 megapascals. Approximately what percentage of cables have a tensile
strength between 425 and 575 megapascals according to the Empirical Rule?
A. 68 percent
B. 95 percent
C. 99.7 percent
D. 50 percent
The Empirical Rule states that for bell-shaped (normally distributed) data, approximately 99.7
percent of observations fall within three standard deviations of the mean. Here, 425 and 575
represent 3 standard deviations below and above the mean (500 minus and plus 3 times 25).
7. A financial analyst is reviewing monthly investment returns. The returns for a specific
stock over four months are 5%, -2%, 4%, and 3%. What is the sample variance of these
returns?
A. 3.50
B. 10.25
C. 15.67
D. 18.25
8. In a university admissions office, the distribution of SAT scores for incoming freshmen is
normally distributed with a mean of 1100 and a standard deviation of 120. If a student
scores a 1250, what is their standardized z-score?
A. 0.83
B. 1.25
C. 1.50
D. 2.10
INTRODUCTION TO STATISTICS-PORTAGE LEARNING –
QUESTIONS AND ANSWERS | VERIFIED AND WELL DETAILED
ANSWERS | PLUS RATIONALES | GUARANTEED PASS | LATEST
EXAM UPDATE | EXAM PREP | STUDY GUIDE | PRACTICE TEST
1. A researcher is analyzing the daily customer wait times at a local bank branch. The data
collected represents the time in minutes for 40 randomly selected customers. Which level of
measurement best describes this wait time data?
A. Nominal level
B. Ordinal level
C. Interval level
D. Ratio level
Ratio level data possesses all the properties of interval data, plus a true, non-arbitrary zero
point representing the complete absence of the characteristic. A wait time of zero minutes
means no wait at all, and ratios between values are meaningful (e.g., a 10-minute wait is twice
as long as a 5-minute wait).
2. A manufacturing plant tracks the defect rate of electronic components produced on
assembly line A versus assembly line B. The line supervisor computes the mean, median,
and mode for each line. If the distribution of defects on assembly line A has a long tail
extending toward higher defect counts, what is the most likely relationship between its
mean and median?
A. The mean is less than the median
B. The mean is equal to the median
C. The mean is greater than the median
D. There is no mathematical relationship between mean and median in skewed distributions
A distribution with a long tail extending toward higher values (positive skew) pulls the mean
in the direction of the tail, making it greater than the median because the mean is sensitive to
extreme values.
3. In a clinical trial for a new cholesterol-lowering medication, patient dropouts due to
adverse side effects are recorded. If a dataset of patient recovery times contains extreme
,outliers caused by underlying genetic anomalies in a few subjects, which measure of center
and spread is most appropriate to report?
A. Mean and standard deviation
B. Median and interquartile range
C. Mode and range
D. Variance and mean absolute deviation
The median and interquartile range are resistant statistics that are minimally affected by
extreme outliers, whereas the mean and standard deviation can be heavily skewed by extreme
data points.
4. An online retailer wants to estimate the average spending of shoppers during a holiday
sale event. They divide the customer database into tiers based on past purchasing history
(Bronze, Silver, Gold, Platinum) and randomly select a proportional number of customers
from each tier. What sampling technique is being utilized?
A. Simple random sampling
B. Systematic sampling
C. Stratified sampling
D. Cluster sampling
Stratified sampling involves dividing the population into homogeneous subgroups (strata)
based on specific characteristics and then drawing a random sample from each stratum to
ensure representation across all groups.
5. A diagnostic test for a rare pulmonary condition has a false positive rate of 5% and a
false negative rate of 2%. If the overall prevalence of the condition in the tested patient
population is 3%, what statistical theorem or rule is necessary to compute the probability
that a patient who tests positive actually has the condition?
A. The Central Limit Theorem
B. Bayes' Theorem
C. Chebyshev's Theorem
D. The Empirical Rule
, Bayes' Theorem provides a mathematical formula for calculating conditional probabilities,
specifically updating the probability of an event (having the condition) given new evidence (a
positive test result) and prior prevalence rates.
6. A quality control engineer measures the tensile strength of steel cables. The distribution
of strengths is approximately bell-shaped with a mean of 500 megapascals and a standard
deviation of 25 megapascals. Approximately what percentage of cables have a tensile
strength between 425 and 575 megapascals according to the Empirical Rule?
A. 68 percent
B. 95 percent
C. 99.7 percent
D. 50 percent
The Empirical Rule states that for bell-shaped (normally distributed) data, approximately 99.7
percent of observations fall within three standard deviations of the mean. Here, 425 and 575
represent 3 standard deviations below and above the mean (500 minus and plus 3 times 25).
7. A financial analyst is reviewing monthly investment returns. The returns for a specific
stock over four months are 5%, -2%, 4%, and 3%. What is the sample variance of these
returns?
A. 3.50
B. 10.25
C. 15.67
D. 18.25
8. In a university admissions office, the distribution of SAT scores for incoming freshmen is
normally distributed with a mean of 1100 and a standard deviation of 120. If a student
scores a 1250, what is their standardized z-score?
A. 0.83
B. 1.25
C. 1.50
D. 2.10
