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.