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Which Car Would You Buy? Suppose that you are in the market to purchase a car. You have narrowed it down to two choices and will let gas mileage be the deciding factor. You decide to conduct a little experiment in which you put 10 gallons of gas in the car and drive it on a closed track until it runs out gas. You conduct this experiment 15 times on each car and record the number of miles driven. Describe each data set. That is, determine the shape, center, and spread. Which car would you buy and why?

We have all heard of the Old Faithful geyser in Yellowstone National Park. However, there is another, less famous, Old Faithful geyser in Calistoga, California. The following data represent the length of eruption (in seconds) for a random sample of eruptions of the California Old Faithful. $$ \begin{array}{rrrrrrr} \hline 108 & 108 & 99 & 105 & 103 & 103 & 94 \\ \hline 102 & 99 & 106 & 90 & 104 & 110 & 110 \\ \hline 103 & 109 & 109 & 111 & 101 & 101 & \\ \hline 110 & 102 & 105 & 110 & 106 & 104 & \\ \hline 104 & 100 & 103 & 102 & 120 & 90 & \\ \hline 113 & 116 & 95 & 105 & 103 & 101 & \\ \hline 100 & 101 & 107 & 110 & 92 & 108 & \\ \hline \end{array} $$ Determine the shape of the distribution of length of eruption by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes the length of eruption?

27\. Rates of Returns of Stocks Stocks may be categorized by sectors. Go to www.pearsonhighered.com/sullivanstats and download \(3_{-} 2_{-} 27\) using the file format of your choice. The data represent the one-year rate of return (in percent) for a sample of consumer cyclical stocks and industrial stocks for the period December 2013 through November 2014 . Note: Consumer cyclical stocks include names such as Starbucks and Home Depot. Industrial stocks include names such as \(3 \mathrm{M}\) and FedEx. (a) Draw a relative frequency histogram for each sector using a lower class limit for the first class of -50 and a class width of \(10 .\) Which sector appears to have more dispersion? (b) Determine the mean and median rate of return for each sector. Which sector has the higher mean rate of return? Which sector has the higher median rate of return? (c) Determine the standard deviation rate of return for each sector. In finance, the standard deviation rate of return is called risk. Typically, an investor "pays" for a higher return by accepting more risk. Is the investor paying for higher returns for these sectors? Do you think the higher returns are worth the cost? Explain.

A survey of 40 randomly selected full-time Joliet Junior College students was conducted in the Fall 2015 semester. In the survey, the students were asked to disclose their weekly spending on entertainment. The results of the survey are as follows: $$ \begin{array}{rrrrrrrr} \hline 21 & 54 & 64 & 33 & 65 & 32 & 21 & 16 \\ \hline 22 & 39 & 67 & 54 & 22 & 51 & 26 & 14 \\ \hline 115 & 7 & 80 & 59 & 20 & 33 & 13 & 36 \\ \hline 36 & 10 & 12 & 101 & 1000 & 26 & 38 & 8 \\ \hline 28 & 28 & 75 & 50 & 27 & 35 & 9 & 48 \\ \hline \end{array} $$ (a) Check the data set for outliers. (b) Draw a histogram of the data and label the outliers on the histogram. (c) Provide an explanation for the outliers.

The Empirical Rule The Stanford-Binet Intelligence Quotient (IQ) measures intelligence. IQ scores have a bellshaped distribution with a mean of 100 and a standard deviation of \(15 .\) (a) What percentage of people has an IQ score between 70 and \(130 ?\) (b) What percentage of people has an IQ score less than 70 or greater than \(130 ?\) (c) What percentage of people has an IQ score greater than \(130 ?\)

A professor has recorded exam grades for 20 students in his class, but one of the grades is no longer readable. If the mean score on the exam was 82 and the mean of the 19 readable scores is \(84,\) what is the value of the unreadable score?

Morningstar is a mutual fund rating agency. It ranks a fund's performance by using one to five stars. A one-star mutual fund is in the bottom \(10 \%\) of its investment class; a five-star mutual fund is at the 90 th percentile of its investment class. Interpret the meaning of a five-star mutual fund.

Lawrence Summers (former Secretary of the Treasury and former president of Harvard) infamously claimed that women have a lower standard deviation IQ than men. He went on to suggest that this was a potential explanation as to why there are fewer women in top math and science positions. Suppose an IQ of 145 or higher is required to be a researcher at a top-notch research institution. Use the idea of standard deviation, the Empirical Rule, and the fact that the mean and standard deviation IQ of humans is 100 and 15 , respectively, to explain Summers' argument.

In December \(2014,\) the average price of regular unleaded gasoline excluding taxes in the United States was \(\$ 3.06\) per gallon, according to the Energy Information Administration. Assume that the standard deviation price per gallon is \(\$ 0.06\) per gallon to answer the following. (a) What minimum percentage of gasoline stations had prices within 3 standard deviations of the mean? (b) What minimum percentage of gasoline stations had prices within 2.5 standard deviations of the mean? What are the gasoline prices that are within 2.5 standard deviations of the mean? (c) What is the minimum percentage of gasoline stations that had prices between \(\$ 2.94\) and \(\$ 3.18 ?\)

According to the U.S. Census Bureau, the mean of the commute time to work for a resident of Boston, Massachusetts, is 27.3 minutes. Assume that the standard deviation of the commute time is 8.1 minutes to answer the following: (a) What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean? (b) What minimum percentage of commuters in Boston has a commute time within 1.5 standard deviations of the mean? What are the commute times within 1.5 standard deviations of the mean? (c) What is the minimum percentage of commuters who have commute times between 3 minutes and 51.6 minutes?