HW module 1.7 (interpreting the mean & standard deviation)
According to the Chebyshev rule, at least 75% of all observations in any data set are contained within how many standard deviations around the mean? A. 3 B. 1 C. 2 D. 4
C. 2
What is the percentage of measurements that are below the 88th percentile? A. 22% B. 12% C. 88% D. cannot determine
C. 88%
Dementia is the loss of intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In an article, two authors explored the experience and struggles of people diagnosed with dementia and their families. The ages of a simple random sample of /x= /x-s= /x-2s= /x-3s= /x+s= /x+2s= /x+3s=
/x= 51.1 /x-s= 43.3 /x-2s= 35.7 /x-3s= 28 /x+s= 58.8 /x+2s= 66.5 /x+3s= 74.2
The quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to answer the following question. A quantitative data set of size 90 has mean 45 and standard deviation 4. Approximately how many observations lie between 41 and 49? Approximately ___________ observations lie between 41 and 49.
0.68 * 90=61.2 --> 62
Decide whether application of the empirical rule is appropriate for curve a.(bell-shape) A. The empirical rule is appropriate. The data set is quantitative and the distribution is roughly bell-shaped, so the empirical rule provides better estimates of the location of the observations than Chebyshev's rule. Your answer is correct. B. The empirical rule is inappropriate. The data set is quantitative, but the distribution is asymmetric. Therefore, Chebyshev's rule provides better estimates of the location of the observations than the empirical rule. C. The empirical rule is appropriate. The data set is quantitative and k is a real number greater than or equal to 1, so the empirical rule provides better estimates of the location of the observations than Chebyshev's rule. D. The empirical rule is inappropriate. The data set is qualitative, so the curve cannot represent the data faithfully. Therefore, Chebyshev's rule provides better estimates of the location of the observations than the empirical rule.
A. The empirical rule is appropriate. The data set is quantitative and the distribution is roughly bell-shaped, so the empirical rule provides better estimates of the location of the observations than Chebyshev's rule.
The heights of the adults in one town have a mean of 67.1 inches and a standard deviation of 3.5 inches. What can you conclude from Chebyshev's theorem about the percentage of adults in the town whose heights are between 60.1 and 74.1 inches? A. The percentage is at least 75%. B. The percentage is at most 75%. C. The percentage is at least 95%. D. The percentage is at most 95%.
A. The percentage is at least 75%.
The distribution of scores on a test is mound-shaped and symmetric with a mean score of 78. If 68% of the scores fall between 72 and 84, which of the following is most likely to be the standard deviation of the distribution? A. 2 B. 6 C. 12 D. 3
B. 6
The systolic blood pressure of 18-year-old women is a roughly bell-shaped distribution with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg? A. 68% B. 95% C. 99.99% D. 99.7%
B. 95%
According to the empirical rule, if the data form a "bell-shaped" normal distribution, what percent of the observations will be contained within 3 standard deviations around the arithmetic mean? A. 95.0 B. 99.7 C. 75.00 D. 68.26
B. 99.7
If the condition for using the empirical rule is met, why should that rule be used instead of Chebyshev's rule? A. Chebyshev's rule is appropriate if the data set is small. If the data set is sufficiently large, then the empirical rule is more appropriate. B. Chebyshev's rule is a lower bound on the proportion of data that can be found within a certain number of standard deviations from the mean. If the distribution is roughly bell-shaped, the empirical rule, in general, provides better estimates than Chebyshev's rule. C. Chebyshev's rule only works for asymmetric distributions. If the distribution is symmetric, then the empirical rule must be used. D. Chebyshev's rule is an approximation to the proportion of data that can be found in any interval around the mean. If the distribution is not bell-shaped, then Chebyshev's rule is equivalent to the empirical rule.
B. Chebyshev's rule is a lower bound on the proportion of data that can be found within a certain number of standard deviations from the mean. If the distribution is roughly bell-shaped, the empirical rule, in general, provides better estimates than Chebyshev's rule.
Decide whether application of the empirical rule is appropriate for curve c. (left-sided) A. The empirical rule is appropriate. The data set is quantitative and k is a real number greater than or equal to 1, so the empirical rule provides better estimates of the location of the observations than Chebyshev's rule. B. The empirical rule is inappropriate. The data set is quantitative, but the distribution is asymmetric. Therefore, Chebyshev's rule provides better estimates of the location of the observations than the empirical rule. Your answer is correct. C. The empirical rule is appropriate. The data set is quantitative and the distribution is roughly bell-shaped, so the empirical rule provides better estimates of the location of the observations than Chebyshev's rule. D. The empirical rule is inappropriate. The data set is qualitative, so the curve cannot represent the data faithfully. Therefore, Chebyshev's rule provides better estimates of the location of the observations than the empirical rule.
B. The empirical rule is inappropriate. The data set is quantitative, but the distribution is asymmetric. Therefore, Chebyshev's rule provides better estimates of the location of the observations than the empirical rule.
Decide whether application of the empirical rule is appropriate for curve b(right side) A. The empirical rule is appropriate. The data set is quantitative and the distribution is roughly bell-shaped, so the empirical rule provides better estimates of the location of the observations than Chebyshev's rule. B. The empirical rule is appropriate. The data set is quantitative and k is a real number greater than or equal to 1, so the empirical rule provides better estimates of the location of the observations than Chebyshev's rule. C. The empirical rule is inappropriate. The data set is quantitative, but the distribution is asymmetric. Therefore, Chebyshev's rule provides better estimates of the location of the observations than the empirical rule. Your answer is correct. D. The empirical rule is inappropriate. The data set is qualitative, so the curve cannot represent the data faithfully. Therefore, Chebyshev's rule provides better estimates of the location of the observations than the empirical rule.
C. The empirical rule is inappropriate. The data set is quantitative, but the distribution is asymmetric. Therefore, Chebyshev's rule provides better estimates of the location of the observations than the empirical rule.
A study was designed to investigate the effects of two variables — (1) a student's level of mathematical anxiety and (2) teaching method — on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 340 with a standard deviation of 30 on a standardized test. Assuming a mound-shaped and symmetric distribution, in what range would approximately 99.7% of the students score? A. below 250 and above 430 B. above 430 C. between 250 and 430 D. below
C. between 250 and 430
Suppose the nightly rate for a three-star hotel in Paris is thought to be bell-shaped and symmetrical with a mean of 160 euros and a standard deviation of 8 euros. The percentage of hotels with rates between 144 and 176 euros is _______. A. approximately 68 B. at least 75 C. at least 89 D. approximately 95
D. approximately 95
Your teacher announces that the scores on a test have a mean of 83 points with a standard deviation of 4 points, so it is reasonable to expect that you scored at least 70 on the test. (T/F)
True
The Empirical Rule applies to distributions that are ________.
symmetric and unimodal.