AP STATISTICS - UNIT 1 PROGRESS
CHECK: MCQ PART B CORRECT 100%
A family has two cats named Gordo and Flaco. Gordo weighs 15 pounds and Flaco
weighs 8 pounds. A cat's weight is classified as unhealthy if the weight is located in the
top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately
normal with mean 9.5 pounds and standard deviation 1.5 pounds. Which of the
following is the best description of Gordo's and Flaco's weights? - ANSWERGordo's
weight is classified as unhealthy but Flaco's weight is not.
WHY?
Because Gordo's weight is over 3 standard deviations above the mean, his weight is in
the top 5% of all weights and is classified as unhealthy. Flaco's weight is less than 2
standard deviations below the mean, so his weight is not in the bottom 5% of all weights
and is not classified as unhealthy.
In the Dominican Republic in August, the distribution of daily high temperature is
approximately normal with mean 86 degrees Fahrenheit (°F). Approximately 95% of all
daily high temperatures are between 83°F and 89°F. What is the standard deviation of
the distribution? - ANSWER1.5°F
WHY?
The empirical rule states that approximately 95% of the observations in a data set that
is approximated by a normal curve will lie within 2 standard deviations of the mean.
Since 95% of all daily high temperatures are between 83°F and 89°F, the interval from
83°F to 89°F has a width of 4 standard deviations (2 above the mean and 2 below the
mean). So 1 standard deviation is (89−83)/4 = 1.5°F
Researchers studying catfish estimated the number of fingerling catfish and large
catfish living in different rivers throughout the country. The following histograms
summarize the relative frequency for each type of catfish.
Based on the histograms, which of the following is the best comparison of the means
and the ranges for the two distributions? - ANSWERThe mean and range of the
fingerling catfish are both greater than those of the large catfish.
WHY?
The range of the distribution of fingerling catfish is between 6,000 and 8,000, while the
range of the distribution of large catfish is between 1,500 and 2,000. Therefore the
range of the distribution of fingerling catfish is greater than the range of the distribution
of large catfish. The least value in the distribution of fingerling catfish is more than the
greatest value of the distribution of large catfish. Therefore the mean of the distribution
of fingerling catfish must be greater than the mean of the distribution of large catfish.
, The following table shows summary statistics, in thousands, for the number of electrical
workers and the number of concrete workers in the construction industry each month for
the past 5 years.
Based on the 1.5 × IQR rule for outliers, which of the following statements is a correct
comparison of the two distributions? - ANSWERThe concrete distribution has at least
one lower outlier, and the electrical distribution has no lower outliers.
WHY?
For the concrete distribution, the minimum of 186 is less than the lower bound of 193.
For the electrical distribution, the minimum of 239 is not less than the lower bound of
215.
A reporter collected data on the purchase prices, in thousands of dollars, of 72 cars sold
in a region. The following histogram summarizes the reporter's data.
For a presentation on the data collected, the reporter used the median of the distribution
to describe the typical purchase price. Which of the following might explain the use of
median to describe the typical purchase price? - ANSWERThere is an outlier between
$80,000 and $85,000. Medians are resistant to outliers, while means are not.
WHY?
Means are not resistant to outliers because their value is influenced by outliers.
Medians are considered resistant because outliers do not greatly affect their value. The
median better represents the typical purchase price.
WHY?
The mean number of miles is the sum of the number of miles divided by the number of
values. The sum of the number of miles is 8+5+7+2+9+8 = 39. The sum of the miles
divided by the number of values is 39/6 = 6.5 miles.
To gather data for a statistics project, a student asked 10 friends how many hours of
sleep they got on the previous night. The data are shown in the following list.
What is the interquartile range (IQR) of the number of hours of sleep shown in the list? -
ANSWER3 hours
WHY?
For the ordered set of data, the third quartile is 8 and the first quartile is 5. The IQR is
the difference of 3.
The distribution of the number of transactions performed at a bank each day is
approximately normal with mean 478 transactions and standard deviation 64
transactions. Which of the following is closest to the proportion of daily transactions
greater than 350? - ANSWER0.977
WHY?
CHECK: MCQ PART B CORRECT 100%
A family has two cats named Gordo and Flaco. Gordo weighs 15 pounds and Flaco
weighs 8 pounds. A cat's weight is classified as unhealthy if the weight is located in the
top 5% or bottom 5% of all cat weights. The distribution of cat weights is approximately
normal with mean 9.5 pounds and standard deviation 1.5 pounds. Which of the
following is the best description of Gordo's and Flaco's weights? - ANSWERGordo's
weight is classified as unhealthy but Flaco's weight is not.
WHY?
Because Gordo's weight is over 3 standard deviations above the mean, his weight is in
the top 5% of all weights and is classified as unhealthy. Flaco's weight is less than 2
standard deviations below the mean, so his weight is not in the bottom 5% of all weights
and is not classified as unhealthy.
In the Dominican Republic in August, the distribution of daily high temperature is
approximately normal with mean 86 degrees Fahrenheit (°F). Approximately 95% of all
daily high temperatures are between 83°F and 89°F. What is the standard deviation of
the distribution? - ANSWER1.5°F
WHY?
The empirical rule states that approximately 95% of the observations in a data set that
is approximated by a normal curve will lie within 2 standard deviations of the mean.
Since 95% of all daily high temperatures are between 83°F and 89°F, the interval from
83°F to 89°F has a width of 4 standard deviations (2 above the mean and 2 below the
mean). So 1 standard deviation is (89−83)/4 = 1.5°F
Researchers studying catfish estimated the number of fingerling catfish and large
catfish living in different rivers throughout the country. The following histograms
summarize the relative frequency for each type of catfish.
Based on the histograms, which of the following is the best comparison of the means
and the ranges for the two distributions? - ANSWERThe mean and range of the
fingerling catfish are both greater than those of the large catfish.
WHY?
The range of the distribution of fingerling catfish is between 6,000 and 8,000, while the
range of the distribution of large catfish is between 1,500 and 2,000. Therefore the
range of the distribution of fingerling catfish is greater than the range of the distribution
of large catfish. The least value in the distribution of fingerling catfish is more than the
greatest value of the distribution of large catfish. Therefore the mean of the distribution
of fingerling catfish must be greater than the mean of the distribution of large catfish.
, The following table shows summary statistics, in thousands, for the number of electrical
workers and the number of concrete workers in the construction industry each month for
the past 5 years.
Based on the 1.5 × IQR rule for outliers, which of the following statements is a correct
comparison of the two distributions? - ANSWERThe concrete distribution has at least
one lower outlier, and the electrical distribution has no lower outliers.
WHY?
For the concrete distribution, the minimum of 186 is less than the lower bound of 193.
For the electrical distribution, the minimum of 239 is not less than the lower bound of
215.
A reporter collected data on the purchase prices, in thousands of dollars, of 72 cars sold
in a region. The following histogram summarizes the reporter's data.
For a presentation on the data collected, the reporter used the median of the distribution
to describe the typical purchase price. Which of the following might explain the use of
median to describe the typical purchase price? - ANSWERThere is an outlier between
$80,000 and $85,000. Medians are resistant to outliers, while means are not.
WHY?
Means are not resistant to outliers because their value is influenced by outliers.
Medians are considered resistant because outliers do not greatly affect their value. The
median better represents the typical purchase price.
WHY?
The mean number of miles is the sum of the number of miles divided by the number of
values. The sum of the number of miles is 8+5+7+2+9+8 = 39. The sum of the miles
divided by the number of values is 39/6 = 6.5 miles.
To gather data for a statistics project, a student asked 10 friends how many hours of
sleep they got on the previous night. The data are shown in the following list.
What is the interquartile range (IQR) of the number of hours of sleep shown in the list? -
ANSWER3 hours
WHY?
For the ordered set of data, the third quartile is 8 and the first quartile is 5. The IQR is
the difference of 3.
The distribution of the number of transactions performed at a bank each day is
approximately normal with mean 478 transactions and standard deviation 64
transactions. Which of the following is closest to the proportion of daily transactions
greater than 350? - ANSWER0.977
WHY?
