91Ó°ÊÓ

The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that weights of all such animals can be described by a Normal model with a standard deviation of 84 pounds. What percent of steers weigh a. over 1250 pounds? b. under 1200 pounds? c. between 1000 and 1100 pounds?

Based on the Normal model \(N(100,15)\) describing IQ scores, what percent of people's IQs would you expect to be a. over \(80 ?\) b. under \(90 ?\) c. between 112 and \(132 ?\)

The Mathematics section of the ACT test had a mean of 20.9 and an SD of 5.3 for the years 2013-2015. If these are well modeled by a Normal distribution, about what percent of students scored a. Over \(31 ?\) b. under \(18 ?\) c. between 18 and \(31 ?\)

The mean household income in the U.S. in 2014 was about \(\$ 72,641\) and the standard deviation was about \(\$ 85,000\). (The median income was \(\$ 51,939 .\) ) If we used the Normal model for these incomes, a. What would be the household income of the top \(1 \% ?\) b. How confident are you in the answer in part a? C. Why might the Normal model not be a good one for incomes?

Here are the summary statistics for the weekly payroll of a small company: lowest salary \(=\$ 300,\) mean salary \(=\$ 700,\) median \(=\$ 500,\) range \(=\$ 1200, \mathrm{IQR}=\$ 600\) first quartile \(=\$ 350,\) standard deviation \(=\$ 400\). a. Do you think the distribution of salaries is symmetric, skewed to the left, or skewed to the right? Explain why. b. Between what two values are the middle \(50 \%\) of the salaries found? c. Suppose business has been good and the company gives every employee a \$50 raise. Tell the new value of each of the summary statistics. d. Instead, suppose the company gives each employee a \(10 \%\) raise. Tell the new value of each of the summary statistics.

A specialty foods company sells "gourmet hams" by mail order. The hams vary in size from 4.15 to 7.45 pounds, with a mean weight of 6 pounds and standard deviation of 0.65 pounds. The quartiles and median weights are \(5.6,6.2,\) and 6.55 pounds. a. Find the range and the IQR of the weights. b. Do you think the distribution of the weights is symmetric or skewed? If skewed, which way? Why? c. If these weights were expressed in ounces \((1\) pound \(=16\) ounces \()\) what would the mean, standard deviation, quartiles, median, IQR, and range be? d. When the company ships these hams, the box and packing materials add 30 ounces. What are the mean, standard deviation, quartiles, median, IQR, and range of weights of boxes shipped (in ounces)? e. One customer made a special order of a 10 -pound ham. Which of the summary statistics of part d might not change if that data value were added to the distribution?

Each year thousands of high school students take either the SAT or the ACT, standardized tests used in the college admissions process. Combined SAT Math and Verbal scores go as high as \(1600,\) while the maximum ACT composite score is \(36 .\) Since the two exams use very different scales, comparisons of performance are difficult. A convenient rule of thumb is \(S A T=40 \times A C T+150\) that is, multiply an ACT score by 40 and add 150 points to estimate the equivalent SAT score. An admissions officer reported the following statistics about the ACT scores of 2355 students who applied to her college one year. Find the summaries of equivalent SAT scores. Lowest score \(=19\) Mean \(=27\) Standard deviation \(=3 \mathrm{Q} 3=30\) Median \(=28 \mathrm{IQF}\)

A high school senior uses the Internet to get information on February temperatures in the town where he'll be going to college. He finds a website with some statistics, but they are given in degrees Celsius. The conversion formula is \(\circ \mathrm{F}=9 / 5 \circ \mathrm{C}+32\). Determine the Fahrenheit equivalents for the summary information below. Maximum temperature \(=11 \circ \mathrm{C}\) Range \(=33\) o Mean \(=1 \circ\) Standard deviation \(=70\) Median \(=2 \circ \mathrm{IQR}=16\)

Corey has 4929 songs in his computer's music library. The songs have a mean duration of 242.4 seconds with a standard deviation of 114.51 seconds. On the Nickel, by Tom Waits, is 380 seconds long. What is its z-score?

The first Stats exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Julie scored a 70 on the first test and a 90 on the second. They both totaled 160 points on the two exams, but Julie claims that her total is better. Explain.