STAT 200 WEEK 6 HOMEWORK PROBLEMS
COMPREHENSIVE SCRIPT 2026 QUESTIONS
WITH SOLUTIONS GRADED A+
◉ which of the following would be information in a question asking
you to find the area of a region under the standard normal curve as a
solution?
a. a probability is given
b. a percentage is given
c. a distance of the horizontal axis is given
d. finding z subscript α Answer: c. a distance of the horizontal axis is
given
◉ what is the difference between a standard normal distribution
and a nonstandard normal distribution? Answer: the standard
normal distribution has a mean of 0 and a standard deviation of 1,
while a nonstandard normal distribution has a different value for
one or both of those parameters
◉ assume that adults have iq scores that are normally distributed
with a mean of 101.9 and a standard deviation of 16.1. find the
probability that a randomly selected adult has an iq greater than
133.3 Answer: 0.0256
,◉ engineers want to design seats in a commercial aircraft so that
they are wide enough to fit 95% of all males. (accommodating 100%
of males would require very wide seats that would be much too
expensive.) men have hip breadths that are normally distributed
with a mean of 14.7 in. and a standard deviation of 1.2 in. find p
subscript 95. that is, find the hip breadth for men that separates the
smallest 95% from the largest 5% Answer: 16.7 in.
◉ which of the following is not true?
a. the area in any normal distribution bounded by some score x is
the same as the area bounded by the equivalent z-score in the
standard normal distribution
b. a z-score is a conversion that standardizes any value from a
normal distribution to a standard normal distribution
c. a z-score is an area under the normal curve
d. if values are converted to standard z-scores, then procedures for
working with all normal distributions are the same as those for the
standard normal distribution Answer: c. a z-score is an area under
the normal curve
◉ where would a value separating the top 15% from other values on
the graph of a normal distribution be found? Answer: the right side
of the horizontal scale of the graph
,◉ what conditions would produce a negative z-score? Answer: a z-
score corresponding to an area located entirely in the left side of the
curve
◉ if you are asked to find the 85th percentile, you are being asked to
find ______ Answer: a data value associated with an area of 0.85 to its
left
◉ what are the unbiased estimators of population parameters?
Answer: sample proportion used to estimate a population
proportion, sample variance used to estimate a population variance,
and sample mean used to estimate a population mean
◉ ________ is the distribution of all values of the statistic when all
possible samples of the same size n are taken from the same
population Answer: the sampling distribution of a statistic
◉ which of the following is not a property of the sampling
distribution of the sample mean?
a. the expected value of the sample mean is equal to the population
mean
b. the sample means target the value of the population mean
c. the distribution of the sample mean tends to be skewed to the
right or left
, d. the mean of the sample means is the population mean Answer: c.
the distribution of the sample mean tends to be skewed to the right
or left
◉ a researcher collects a simple random sample of grade-point
averages of statistics students, and she calculated the mean of this
sample. under what conditions can that sample mean be treated as a
value from a population having a normal distribution? Answer: if the
population of grade-point averages has a normal distribution and
the sample has more than 30 grade-point averages
◉ weights of golden retriever dogs are normally distributed.
samples of weights of golden retriever dogs, each of size n = 15, are
randomly collected and the sample means are found. is it correct to
conclude that the sample means cannot be treated as being from a
normal distribution because the sample size is too small? Answer:
no; the original population is normally distributed, so the sample
means will be normally distributed for any sample size
◉ the ______ tells us that for a population with any distribution, the
distribution of the sample means approaches a normal distribution
as the sample size increases Answer: central limit theorem
◉ the standard deviation of the distribution of sample means is _____
Answer: σ over the square root of n
COMPREHENSIVE SCRIPT 2026 QUESTIONS
WITH SOLUTIONS GRADED A+
◉ which of the following would be information in a question asking
you to find the area of a region under the standard normal curve as a
solution?
a. a probability is given
b. a percentage is given
c. a distance of the horizontal axis is given
d. finding z subscript α Answer: c. a distance of the horizontal axis is
given
◉ what is the difference between a standard normal distribution
and a nonstandard normal distribution? Answer: the standard
normal distribution has a mean of 0 and a standard deviation of 1,
while a nonstandard normal distribution has a different value for
one or both of those parameters
◉ assume that adults have iq scores that are normally distributed
with a mean of 101.9 and a standard deviation of 16.1. find the
probability that a randomly selected adult has an iq greater than
133.3 Answer: 0.0256
,◉ engineers want to design seats in a commercial aircraft so that
they are wide enough to fit 95% of all males. (accommodating 100%
of males would require very wide seats that would be much too
expensive.) men have hip breadths that are normally distributed
with a mean of 14.7 in. and a standard deviation of 1.2 in. find p
subscript 95. that is, find the hip breadth for men that separates the
smallest 95% from the largest 5% Answer: 16.7 in.
◉ which of the following is not true?
a. the area in any normal distribution bounded by some score x is
the same as the area bounded by the equivalent z-score in the
standard normal distribution
b. a z-score is a conversion that standardizes any value from a
normal distribution to a standard normal distribution
c. a z-score is an area under the normal curve
d. if values are converted to standard z-scores, then procedures for
working with all normal distributions are the same as those for the
standard normal distribution Answer: c. a z-score is an area under
the normal curve
◉ where would a value separating the top 15% from other values on
the graph of a normal distribution be found? Answer: the right side
of the horizontal scale of the graph
,◉ what conditions would produce a negative z-score? Answer: a z-
score corresponding to an area located entirely in the left side of the
curve
◉ if you are asked to find the 85th percentile, you are being asked to
find ______ Answer: a data value associated with an area of 0.85 to its
left
◉ what are the unbiased estimators of population parameters?
Answer: sample proportion used to estimate a population
proportion, sample variance used to estimate a population variance,
and sample mean used to estimate a population mean
◉ ________ is the distribution of all values of the statistic when all
possible samples of the same size n are taken from the same
population Answer: the sampling distribution of a statistic
◉ which of the following is not a property of the sampling
distribution of the sample mean?
a. the expected value of the sample mean is equal to the population
mean
b. the sample means target the value of the population mean
c. the distribution of the sample mean tends to be skewed to the
right or left
, d. the mean of the sample means is the population mean Answer: c.
the distribution of the sample mean tends to be skewed to the right
or left
◉ a researcher collects a simple random sample of grade-point
averages of statistics students, and she calculated the mean of this
sample. under what conditions can that sample mean be treated as a
value from a population having a normal distribution? Answer: if the
population of grade-point averages has a normal distribution and
the sample has more than 30 grade-point averages
◉ weights of golden retriever dogs are normally distributed.
samples of weights of golden retriever dogs, each of size n = 15, are
randomly collected and the sample means are found. is it correct to
conclude that the sample means cannot be treated as being from a
normal distribution because the sample size is too small? Answer:
no; the original population is normally distributed, so the sample
means will be normally distributed for any sample size
◉ the ______ tells us that for a population with any distribution, the
distribution of the sample means approaches a normal distribution
as the sample size increases Answer: central limit theorem
◉ the standard deviation of the distribution of sample means is _____
Answer: σ over the square root of n
