ECN 221 Foster Exam #2 Questions and Answers with Verified
Solutions | Latest 2026 Update
Q: Normal Probability Distributions
Answer:
The most important distribution for describing a
continuous random variable. It is widely used in statistical inference. It has been used
in a wide
variety of applications including height of people, test scores, rainfall amounts,
scientific
measurements.
Q: Uniform Probability Distributions
Answer:
A random variable is uniformly distributed whenever the
probability is proportional to the interval's length. The uniform probability density
function is:
f(x)=1/(b-a) for a <= x <= b and =0 elsewhere where a = smallest value the variable
can assume
and b= largest value the variable can assume.
, ECN 221 Foster Exam #2 Questions and Answers with Verified
Solutions | Latest 2026 Update
Q: The Normal Random Variable
Answer:
Probabilities for the normal random variable are given by
areas under the curve. The total area under the curve is 1 (.5 to the left of the mean
and .5 to
the right)
Q: Empirical Rule
Answer:
68.3% of values of a normal random variable are within +/-1 standard
deviation of its mean. 95.4% of values of a normal random variable are within +/-2
standard
deviation of its mean. 99.7% of values of a normal random variable are within +/-3
standard
deviation of its mean.
, ECN 221 Foster Exam #2 Questions and Answers with Verified
Solutions | Latest 2026 Update
Q: Exponential Probability Distribution
Answer:
Useful in describing the time it takes to complete a task.
The exponential random variables can be used to describe: Time between vehicle
arrivals at a
toll booth. Tie required to complete a questionnaire. Distance between major defects
in a
highway. In waiting line applications, the exponential distribution is often used for
service
times. A property of the exponential distribution is that the mean and standard
deviation are
equal. The exponential distribution is skewed to the right. Its skewness measure is 2.
Q: Selecting a sample
Answer:
Reasons why we select a sample is to collect data to answer a research
question about a population. The sample results provide only estimates of the
population
characteristics. The reason is simply that the sample contains only a portion of the
population.
, ECN 221 Foster Exam #2 Questions and Answers with Verified
Solutions | Latest 2026 Update
Q: Standard Normal Probability Distributions
Answer:
A random variable having a normal distribution
with a mean of 0 and a standard deviation of 1 is said to have a standard normal
probability
distribution. To convert to standard normal: Z= x-µ / σ
Q: Elements, Population, Sample, Target and Sampled populations, and Frames
Answer:
Element; the
entity on which data are collected. Population; a collection of all the elements of
interest.
Sample; a subset of the population. Sampled population; the population from which
the sample
is drawn. Frame; a list of all the elements that the sample will be selected from.
Solutions | Latest 2026 Update
Q: Normal Probability Distributions
Answer:
The most important distribution for describing a
continuous random variable. It is widely used in statistical inference. It has been used
in a wide
variety of applications including height of people, test scores, rainfall amounts,
scientific
measurements.
Q: Uniform Probability Distributions
Answer:
A random variable is uniformly distributed whenever the
probability is proportional to the interval's length. The uniform probability density
function is:
f(x)=1/(b-a) for a <= x <= b and =0 elsewhere where a = smallest value the variable
can assume
and b= largest value the variable can assume.
, ECN 221 Foster Exam #2 Questions and Answers with Verified
Solutions | Latest 2026 Update
Q: The Normal Random Variable
Answer:
Probabilities for the normal random variable are given by
areas under the curve. The total area under the curve is 1 (.5 to the left of the mean
and .5 to
the right)
Q: Empirical Rule
Answer:
68.3% of values of a normal random variable are within +/-1 standard
deviation of its mean. 95.4% of values of a normal random variable are within +/-2
standard
deviation of its mean. 99.7% of values of a normal random variable are within +/-3
standard
deviation of its mean.
, ECN 221 Foster Exam #2 Questions and Answers with Verified
Solutions | Latest 2026 Update
Q: Exponential Probability Distribution
Answer:
Useful in describing the time it takes to complete a task.
The exponential random variables can be used to describe: Time between vehicle
arrivals at a
toll booth. Tie required to complete a questionnaire. Distance between major defects
in a
highway. In waiting line applications, the exponential distribution is often used for
service
times. A property of the exponential distribution is that the mean and standard
deviation are
equal. The exponential distribution is skewed to the right. Its skewness measure is 2.
Q: Selecting a sample
Answer:
Reasons why we select a sample is to collect data to answer a research
question about a population. The sample results provide only estimates of the
population
characteristics. The reason is simply that the sample contains only a portion of the
population.
, ECN 221 Foster Exam #2 Questions and Answers with Verified
Solutions | Latest 2026 Update
Q: Standard Normal Probability Distributions
Answer:
A random variable having a normal distribution
with a mean of 0 and a standard deviation of 1 is said to have a standard normal
probability
distribution. To convert to standard normal: Z= x-µ / σ
Q: Elements, Population, Sample, Target and Sampled populations, and Frames
Answer:
Element; the
entity on which data are collected. Population; a collection of all the elements of
interest.
Sample; a subset of the population. Sampled population; the population from which
the sample
is drawn. Frame; a list of all the elements that the sample will be selected from.
