Chapter 6: Q. 6.77 (page 269)
Determine
Short Answer
The score under the usual normal curve with the area to its right is around .
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Chapter 6: Q. 6.77 (page 269)
Determine
The score under the usual normal curve with the area to its right is around .
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A variable is normally distributed with a mean and standard deviation . Find the percentage of all possible values of the variable that
a. lie between and
b. exceed
c. are less than .
Use Table II to obtain the areas under the standard normal curve required in Exercises 6.59-6.66. Sketch a standard normal curve and shade the area of interest in each problem.
6.60 Determine the area under the standard normal curve that lies to the left of
a.
b.
c. .
Each year, thousands of high school students bound for college take the Scholastic Assessment Test (SAT). This test measures the verbal and mathematical abilities of prospective college students. Student scores are reported on a scale that ranges from a low of to a high of . Summary results for the scores are published by the College Entrance Examination Board in College Bound Seniors. In one high school graduating class, the SAT scores are as provided on the WeissStats site. Use the technology of your choice to answer the following questions.
a. Do the SAT verbal scores for this class appear to be approximately normally distributed? Explain your answer.
b. Do the SAT math scores for this class appear to be approximately normally distributed? Explain your answer.
The area under a density curve that lies to the left of 60 is . What percentage of all possible observations of the variable are
a. Less than 60?
b. At least 60?
6.31 Waiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve for , and otherwise.
a. Graph the density curve of this variable.
b. Show that the area under this density curve to the left of any number between 0 and 30 equals .
What percentage of the time does John wait for the train
c. less than 5 minutes?
d. between 10 and 15 minutes?
e. at least 20 minutes?
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