Foreign-born residents The cumulative relative frequency graph shows the distribution of the percent of foreign-born residents in the states.
a. Estimate the interquartile range (IQR) of this distribution. Show your method.
b. What is the percentile for Arizona, which had foreign-born residents that year?
c. Explain why the graph is fairly flat between and
d. Draw the histogram that corresponds to this graph.
Part (a) The value is
Part (b) The percentile is
Part (c) The cumulative relative frequency for these values is growing between and percent.
Part (d) The histogram is
The plot is:
The percentile of an individual is the percentage of the distribution that is less than the data value of the individual.
The third quartile and first quartile, according to the plot, are and respectively.
Thus, the interquartile range is:
Thus, the required value is
Create a vertical line that cuts the axis at to calculate the required percentage. Create a horizontal line to connect the vertical and horizontal lines. Both lines overlap at the percentile, as can be seen.
Thus, the required percentile is
Because of the minor rise in frequency for these values, the cumulative relative frequency for these values is growing between and percent.
The histogram could be constructed as:
The number of absences during the fall semester was recorded for each student in a large elementary school. The distribution of absences is displayed in the following cumulative relative frequency graph.
If the distribution of absences was displayed in a histogram, what would be the best description of the histogram’s shape?
c. Skewed left
d. Skewed right
e. Cannot be determined
The army reports that the distribution of head circumference among male soldiers is approximately Normal with mean of inches and standard deviation inches.
(a) A male soldier whose head circumference is -inches would be at what percentile? Show your method clearly.
(b) The army’s helmet supplier regularly stocks helmets that fit male soldiers with head circumferences between and inches. Anyone with a head circumference outside that interval requires a customized helmet order. What percent of male soldiers require custom helmets? Show your work, including a well-labeled sketch of a Normal curve.
(c) Find the interquartile range for the distribution of head circumference among male soldiers. Show your method clearly.
Multiple choice: Select the best answer. Mark receives a score report detailing his performance on a statewide test. On the math section, Mark earned a raw score of , which placed him at the 68th percentile. This means that
(a) Mark did better than about of the students who took the test.
(b) Mark did worse than about of the students who took the test.
(c) Mark did better than about of the students who took the test.
(d) Mark did worse than about of the students who took the test.
(e) Mark got fewer than half of the questions correct on this test.
Big sharks Here are the lengths (in feet) of 44 great white sharks:
A dot plot of the data and summary statistics are shown below. Is this distribution of shark length approximately Normal? Justify your answer based on the graph and the 68–95–99.7 rule.
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