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A sociologist says, "Typically, men in the United States still earn more than women." What does this statement mean? (Pick the best choice.) a. All men make more than all women in the United States. b. All U.S. women's salaries are less varied than all men's salaries. c. The center of the distribution of salaries for U.S. men is greater than the center for women. d. The highest-paid people in the United States are men.

The tuition costs (in dollars) for a sample of four-year state colleges in California and Texas are shown below. Compare the means and the standard deviations of the data and compare the state tuition costs of the two states in a sentence or two. CA: \(7040,6423,6313,6802,7048,7460\) TX: \(7155,7504,7328,8230,7344,5760\)

The mean weight gain for women during a full-term pregnancy is \(30.2\) pounds. The standard deviation of weight gain for this group is \(9.9\) pounds, and the shape of the distribution of weight gains is symmetric and unimodal. a. State the weight gain for women one standard deviation below the mean and for one standard deviation above the mean. b. Is a weight gain of 35 pounds more or less than one standard deviation from the mean?

The mean birth length for U.S. children born at full term (after 40 weeks) is \(52.2\) centimeters (about \(20.6\) inches). Suppose the standard deviation is \(2.5\) centimeters and the distributions are unimodal and symmetric. a. What is the range of birth lengths (in centimeters) of U.S.-bom children from one standard deviation below the mean to one standard deviation above the mean? b. Is a birth length of 54 centimeters more than one standard deviation above the mean?

Four siblings are \(2,6,9\), and 10 years old. a. Calculate the mean of their current ages. Round to the nearest tenth. b. Without doing any calculation, predict the mean of their ages 10 years from now. Check your prediction by calculating their mean age in 10 years (when they are \(12,16,19\), and 20 years old). c. Calculate the standard deviation of their current ages. Round to the nearest tenth. d. Without doing any calculation, predict the standard deviation of their ages 10 years from now. Check your prediction by calculating the standard deviation of their ages in 10 years. c. Adding 10 years to each of the siblings ages had different effects on the mean and the standard deviation. Why did one of these values change while the other remained unchanged? How does adding the same value to cach number in a data set affect the mean and standard deviation?

In the most recent summer Olympics, do you think the standard deviation of the running times for all men who ran the 100 -meter race would be larger or smaller than the standard deviation of the running times for the men's marathon? Explain.

Data on residential energy consumption per capita (measured in million BTU) had a mean of \(70.8\) and a standard deviation of \(7.3\) for the states east of the Mississippi River. Assume that the distribution of residential energy use if approximately unimodal and symmetric. a. Between which two values would you expect to find about \(68 \%\) of the per capita energy consumption rates? b. Between which two values would you expect to find about \(95 \%\) of the per capita energy consumption rates? c. If an eastern state had a per capita residential energy consumption rate of 54 million BTU, would you consider this unusual? Explain. d. Indiana had a per capita residential energy consumption rate of \(80.5\) million BTU. Would you consider this unusually high? Explain.

In 2017 a pollution index was calculated for a sample of cities in the eastern states using data on air and water pollution. Assume the distribution of pollution indices is unimodal and symmetric. The mean of the distribution was \(35.9\) points with a standard deviation of \(11.6\) points. (Source: numbeo. com) see Guidance page \(142 .\) a. What percentage of eastern cities would you expect to have a pollution index between \(12.7\) and \(59.1\) points? b. What percentage of castern cities would you expect to have a pollution index between \(24.3\) and \(47.5\) points? c. The pollution index for New York, in 2017 was \(58.7\) points. Based on this distribution, was this unusually high? Explain.

In 2017 a pollution index was calculated for a sample of cities in the western states using data on air and water pollution. Assume the distribution of pollution indices is unimodal and symmetric. The mean of the distribution was \(43.0\) points with a standard deviation of \(11.3\) points. a. What percentage of western cities would you expect to have a pollution index between \(31.7\) and \(54.3\) points? b. What percentage of western cities would you expect to have a pollution index between \(20.4\) and \(65.6\) ? c. The pollution index for San Jose in 2017 was \(51.9\) points. Based on this distribution, was this unusually high? Explain.

The dotplot shows heights of college women; the mean is 64 inches \((5\) feet 4 inches), and the standard deviation is 3 inches. a. What is the \(z\) -score for a height of 58 inches ( 4 feet 10 inches)? b. What is the height of a woman with a z-score of \(1 ?\)