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Chapter 2: Q 35. (page 108)
Scores on the ACT college entrance exam follow a bell-shaped distribution with mean and standard deviation 5. Wayne’s standardized score on the ACT was What was Wayne’s actual ACT score?
a.
b.
c. 1
d.
e.
The correct option is (d)
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Measure up Clarence measures the diameter of each tennis ball in a bag with a standard ruler. Unfortunately, he uses the ruler incorrectly so that each of his measurements is too large. Clarence’s data had a mean of and a standard deviation of (Recall that )
a. Find the mean of the corrected measurements in centimeters.
b. Calculate the standard deviation of the corrected measurements in centimeters.
Teacher raises A school system employs teachers at salaries between and Page Number: The teachers’ union and school board are negotiating the form of next year’s increase in the salary schedule. Suppose that every teacher is given a raise. What effect will these raises have on each of the following characteristics of the resulting distribution of salary?
a. Shape
b. Mean and median
c. Standard deviation and interquartile range (IQR)
Where’s the bus? Sally takes the same bus to work every morning. The
amount of time (in minutes) that she has to wait for the bus can be modeled by a uniform distribution on the interval from minutes to minutes.
a. Draw a density curve to model the amount of time that Sally has to wait for the bus. Be sure to include scales on both axes.
b. On what percent of days does Sally wait between and minutes for the bus?
c. Find the percentile of Sally’s wait times.
Step right up! Refer to Exercise Suppose that the distances from the tops of the students’ heads to the ground are converted from inches to feet (note that ).
a. What shape would the resulting distribution have? Explain your answer.
b. Find the mean of the distribution of distance in feet.
c. Find the standard deviation of the distribution of distance in feet.
Outliers The percent of the observations that are classified as outliers by the rule is the same in any Normal distribution. What is this percent? Show your method clearly.
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