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Age at diagnosis for each of 20 patients under treatment for meningits was given in a research paper. Suppose the ages (in years) were as follows. 18 18 25 19 23 20 63 18 21 18 20 18 18 20 18 19 | 28 17 18 18 A USE SALT

Age at diagnosis for each of 20 patients under treatment for meningits was given in a research paper. Suppose the ages (in years) were as follows. 18 18 25 19 23 20 63 18 21 18 20 18 18 20 18 19 | 28 17 18 18 A USE SALT

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Age at diagnosis for each of 20 patients under treatment for meningitis was given in a research paper. Suppose the ages (in years) were as follows. 18 18 25 19 23 20 63 18 21 18 20 18 18 20 18 19 28 17 18 18 A USE SALT (a) Calculate the values of the sample mean and the standard deviation. (Round your standard deviation to four decimal places.) 21.85 10.0696 sample mean v yr standard deviation v yr (b) Compute the upper quartile, the lower quartile, and the interquartile range. upper quartile lower quartile 20.75 v yr 18 v yr interquartile range 2.75 X yr
Transcribed Image Text:Age at diagnosis for each of 20 patients under treatment for meningitis was given in a research paper. Suppose the ages (in years) were as follows. 18 18 25 19 23 20 63 18 21 18 20 18 18 20 18 19 28 17 18 18 A USE SALT (a) Calculate the values of the sample mean and the standard deviation. (Round your standard deviation to four decimal places.) 21.85 10.0696 sample mean v yr standard deviation v yr (b) Compute the upper quartile, the lower quartile, and the interquartile range. upper quartile lower quartile 20.75 v yr 18 v yr interquartile range 2.75 X yr
In a study investigating the effect of car speed on accident severity, 5,000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5,000 accidents, the average speed was 54 mph and the standard deviation was 11 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. (Use the Empirical Rule.) (a) Approximately what percentage of these vehicle speeds were between 43 and 65 mph? (b) Approximately what percentage of these vehicle speeds exceeded 65 mph? Step 1 (a) Approximately what percentage of these vehicle speeds were between 43 and 65 mph? Recall that per the Empirical Rule, if a data distribution is mound shaped and approximately symmetric, then: • Approximately 68% of the observations fall within 1 standard deviation of the mean. • Approximately 95% of the observations fall within 2 standard deviations of the mean. • Approximately 99.7% of the observations fall within 3 standard deviations of the mean. For this data distribution, it is given that the mean and standard deviation are x = 54 and s = 11. To find the approximate percentage of the vehicle speeds that were between 43 mph and 65 mph, first calculate how far 43 mph and 65 mph are from the mean. distance between the lower value and the mean = 43 43 - 54 - -11 -11 distance between the mean and the upper value = 65 5 - 54 = 11 11 Step 2 For the range 43 to 65 mph, the lower value is 11 less than the mean, and the upper value is 11 more than the mean. In other words, 43 is 1 standard deviation 1 standard deviation below the mean, and 65 is 1 standard deviation 1 standard deviation above the mean. This means that approximately 68 68 % of the vehicle speeds of fatal accidents at impact fall between the lower value of 43 mph and the upper value of 65 mph. Step 3 (b) Approximately what percentage of these vehicle speeds exceeded 65 mph? We previously found that 65 mph is 1 standard deviation above the mean. To find the approximate percentage of the vehicle speeds that exceed 65 mph, we must find the approximate percentage of values that are more than 1 standard deviation above the mean. Recall that the approximate percentages given by the Empirical Rule are described in the figure below. approximate percentages implied by the Empirical Rule 34% 34% 2.35% 2.35% 13.5% 13.5% -3 sd -2 sd -1 sd +1 sd +2 sd +3 sd I sd I sd Mean This means that we are interested in the percentage of values which are between the lower value of 1 standard deviation 1 standard deviation above the mean and the higher value of 3 standard deviations 3 standard deviations above the mean. Step 4 In other words, to calculate the percentage of values that are greater than 1 standard deviation from the mean, we must add the percentage of values between 1 standard deviation above the mean and 2 standard deviations above the mean to the percentage of values between 2 standard deviations above the mean and 3 standard deviations above the mean. approximate percentages implied by the Empirical Rule 34% 34% 2.35% 2.35% 13.5% 13.5% -3 sd -2 sd 1 sd +1 sd +2 sd +3 sd I sd I sd Mean percentage of values more than 1 standard deviation above the mean = % + 2.35% Therefore, the percentage of vehicle speeds greater than 65 mph, rounded to the nearest whole number, is %.
Transcribed Image Text:In a study investigating the effect of car speed on accident severity, 5,000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5,000 accidents, the average speed was 54 mph and the standard deviation was 11 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal. (Use the Empirical Rule.) (a) Approximately what percentage of these vehicle speeds were between 43 and 65 mph? (b) Approximately what percentage of these vehicle speeds exceeded 65 mph? Step 1 (a) Approximately what percentage of these vehicle speeds were between 43 and 65 mph? Recall that per the Empirical Rule, if a data distribution is mound shaped and approximately symmetric, then: • Approximately 68% of the observations fall within 1 standard deviation of the mean. • Approximately 95% of the observations fall within 2 standard deviations of the mean. • Approximately 99.7% of the observations fall within 3 standard deviations of the mean. For this data distribution, it is given that the mean and standard deviation are x = 54 and s = 11. To find the approximate percentage of the vehicle speeds that were between 43 mph and 65 mph, first calculate how far 43 mph and 65 mph are from the mean. distance between the lower value and the mean = 43 43 - 54 - -11 -11 distance between the mean and the upper value = 65 5 - 54 = 11 11 Step 2 For the range 43 to 65 mph, the lower value is 11 less than the mean, and the upper value is 11 more than the mean. In other words, 43 is 1 standard deviation 1 standard deviation below the mean, and 65 is 1 standard deviation 1 standard deviation above the mean. This means that approximately 68 68 % of the vehicle speeds of fatal accidents at impact fall between the lower value of 43 mph and the upper value of 65 mph. Step 3 (b) Approximately what percentage of these vehicle speeds exceeded 65 mph? We previously found that 65 mph is 1 standard deviation above the mean. To find the approximate percentage of the vehicle speeds that exceed 65 mph, we must find the approximate percentage of values that are more than 1 standard deviation above the mean. Recall that the approximate percentages given by the Empirical Rule are described in the figure below. approximate percentages implied by the Empirical Rule 34% 34% 2.35% 2.35% 13.5% 13.5% -3 sd -2 sd -1 sd +1 sd +2 sd +3 sd I sd I sd Mean This means that we are interested in the percentage of values which are between the lower value of 1 standard deviation 1 standard deviation above the mean and the higher value of 3 standard deviations 3 standard deviations above the mean. Step 4 In other words, to calculate the percentage of values that are greater than 1 standard deviation from the mean, we must add the percentage of values between 1 standard deviation above the mean and 2 standard deviations above the mean to the percentage of values between 2 standard deviations above the mean and 3 standard deviations above the mean. approximate percentages implied by the Empirical Rule 34% 34% 2.35% 2.35% 13.5% 13.5% -3 sd -2 sd 1 sd +1 sd +2 sd +3 sd I sd I sd Mean percentage of values more than 1 standard deviation above the mean = % + 2.35% Therefore, the percentage of vehicle speeds greater than 65 mph, rounded to the nearest whole number, is %.
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