Suppose that the national average for the math portion of the College Board's SAT is 516. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

In a study investigating the effect of car speed on accident severity, the vehicle speed at impact was recorded for 5000 fatal accidents. For these accidents, the mean speed was 42 miles per hour with a standard deviation of 15 miles per hour. Assuming the speeds are normally distributed, use the empirical rule to answer the following: a) About what percent of vehicle speeds were between 42 and 72 miles per hour? b) About what percent of vehicle speeds were in excess of 57 miles per hour? c) About what percent of vehicle speeds were below 12 miles per hour? d) About what percent of vehicle speeds were between 12 miles per hour and 57 miles per hour?

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1259 with a standard deviation of 29 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.

(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between  and  A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between  and  A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between  and  A.D.

Suppose that the national average for the math portion of the College Board's SAT is 531. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 631?

(b) What percentage of students have an SAT math score greater than 731?

(c) What percentage of students have an SAT math score between 431 and 531?

(d) What is the z-score for student with an SAT math score of 630?

(e) What is the z-score for a student with an SAT math score of 395?

Suppose that the national average for the math portion of the College Board's SAT is 520. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 595?

(b) What percentage of students have an SAT math score greater than 670?

(c) What percentage of students have an SAT math score between 445 and 520?

(d) What is the z-score for student with an SAT math score of 635?

(e) What is the z-score for a student with an SAT math score of 425?

Real estate purchases are often financed with at least 80% debt. Most​ corporations, however, have less than 50% debt financing. Assuming that firms decide their capital structure by considering the tradeoff between the tax benefits of debt and the costs of financial distress, which of the following provides the most plausible explanation for this empirical observation?

Group of answer choices

The tax savings from debt are likely to be much higher for real estate transactions than for corporations.

Real estate assets can generally be easily resold at their full market​ value, whereas corporations typically face much higher distress costs.

It is impossible to finance real estate purchases using equity.

The financial distress costs of corporations are low because corporate assets are easy to​ liquidate, whereas real estate assets are difficult to resell.

Problem 2-23

Suppose that the national average for the math portion of the College Board's SAT is 525. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

Problem 2-23

Suppose that the national average for the math portion of the College Board's SAT is 534. The College Board periodically rescales the test scores such that the standard deviation is approximately 50. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

9. The mean value of land and buildings per acre from a sample of farms is ​$1700, with a standard deviation of ​$200. The data set has a​ bell-shaped distribution. Assume the number of farms in the sample is 73.

A. Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1300 and ​$2100.

B. If 21 additional farms were​ sampled, about how many of these additional farms would you expect to have land and building values between $1300 per acre and ​$2100 per​ acre?

10. From a sample with n=28​, the mean number of televisions per household is 2 with a standard deviation of 1 television. Using Chebychev's Theorem, determine at least how many of the households have between 0 and 4 televisions.