Exam 5: The Standard Deviation As a Ruler and the Normal Model

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Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 132 minutes,mean = 76 minutes,median = 76 minutes,range = 102 minutes,IQR = 62,Q1 = 30,standard deviation = 10 minutes.Between what two values are the middle 50% of times?

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the highest 7%

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The freethrow percentages for the participants in a basketball tournament were compiled.The percents ranged from 33% to 99% with a mean of 56% and a standard deviation of 7%.The quartiles and median percentages were 43%,87%,and 56%.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

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A basketball coach kept statistics for his team in free throw percentage and steals (among others).At the last game,Erin's free throw percentage was 79% and she had 4 steals.The team averaged 90% from the free throw line with a standard deviation of 6% and they averaged 7 steals with a standard deviation of 4.In which category did Erin do better compared with her team? Explain.

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The setter on your school's volleyball team average 58 assists per match with a standard deviation of 6.How many standard deviations from the mean is an outing with 79 assists?

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the middle 87.4%

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σ = 150,9.18% below 900;μ = ?

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The average speed cars travel on a road is 77 km/h.A car travelling 60 km/h has a z-score of -1.7.Find the standard deviation.

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For a recent English exam,use the Normal model N(73,9.2)to find the percent of scores under 58.Round to the nearest tenth of a percent.

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Here are the weekly winnings for several local poker players: $100,$50,$125,$75,$80,$60,$110,$150,$300,$700,$115,$75,$1000,$5000.Which is a better summary of the spread,the standard deviation or the IQR? Explain.

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0 < z < 3.01

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You heard that the average number of years of experience among stockbrokers is 14 years.You can't remember the standard deviation somebody with 8 years experience has a z-score of -2.Find the standard deviation.

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Here are some statistics for the annual Wildcat golf tournament: lowest score = 56,mean score = 90,median = 98,range = 94,IQR = 106,Q1 = 36,standard deviation = 11.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

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Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest amount = 18 cm,mean = 49 cm,median = 42 cm,range = 82 cm,IQR = 50,Q1 = 20,standard deviation = 10 cm.Between what two values are the middle 50% of snowfall found?

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For a recent English exam,use the Normal model N(73,9.2)to find the percent of scores over 85.Round to the nearest tenth of a percent.

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σ = 10,68% below 200;μ = ?

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the highest 9%

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An English instructor gave a final exam and found a mean score of 70 points and a standard deviation of 6.8 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Describe the scores of the top 2.5%.

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Based on the Normal model for car speeds (in km/h)on a road N(77,9.1),what is the cutoff value for the highest 15% of the speeds?

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A town's average snowfall is 40 cm per year with a standard deviation of 12 cm.How many standard deviations from the mean is a snowfall of 64 cm?

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