Problem 1
A company selling clothing on the Internet reports that the packages it ships have a median weight of 68 ounces and an IQR of 40 ounces. a) The company plans to include a sales flyer weighing 4 ounces in each package. What will the new median and IQR be? b) If the company recorded the shipping weights of these new packages in pounds instead of ounces, what would the median and IQR be? \((1 \mathrm{lb} .=16 \mathrm{oz}\).)
Problem 2
A company's customer service hotline handles many calls relating to orders, refunds, and other issues. The company's records indicate that the median length of calls to the hotline is \(4.4\) minutes with an IQR of \(2.3\) minutes. a) If the company were to describe the duration of these calls in seconds instead of minutes, what would the median and IQR be? b) In an effort to speed up the customer service process, the company decides to streamline the series of pushbutton menus customers must navigate, cutting the time by 24 seconds. What will the median and IQR of the length of hotline calls become?
Problem 3
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.
Problem 4
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?
Problem 5
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 \(=19 \quad\) Mean \(=27\) Standard deviation \(=3\) \(\mathrm{Q} 3=30\) Median \(=28 \quad \mathrm{IQR}=6\)
Problem 6
A high school senior uses the Internet to get information on February temperatures in the town where hell be going to college. He finds a Web site 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 \(=11^{\circ} \mathrm{C} \quad\) Range \(=33^{\circ}\) Mean \(=1^{\circ} \quad\) Standard deviation \(=7^{\circ}\) Median \(=2^{\circ} \quad\) IQR \(=16^{\circ}\)
Problem 7
Suppose your Statistics professor reports test grades as z-scores, and you got a score of \(2.20\) on an exam. Write a sentence explaining what that means.
Problem 8
One of the authors has an adopted grandson whose birth family members are very short. After examining him at his 2 -year checkup, the boy's pediatrician said that the \(z\) -score for his height relative to American 2-year-olds was \(-1.88\). Write a sentence explaining what that means.
Problem 9
The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Gregor's z-score was \(-2\). How many points did he score?
Problem 10
People with \(z\) -scores above \(2.5\) on an IQ test are sometimes classified as geniuses. If IQ scores have a mean of 100 and a standard deviation of 16 points, what IQ score do you need to be considered a genius?
