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Chapter 9 Review Exercises

Chapter 9 Review Exercises
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  • 15. Distribution of Numbers of Hotel Rooms Occupied

    The histogram shows the distribution of the numbers of hotel rooms occupied for 150 days in a year. Does this data set have a normal distribution? Explain your reasoning.

    • Worked-Out Solution

      The shape of the distribution is approximately bell-shaped, so the data appears to have a normal distribution.

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     _____     _    _     ______   _    _     _  __  
    |  __ \\  | || | ||  /_____// | || | ||  | |/ // 
    | |  \ || | || | ||  `____ `  | || | ||  | ' //  
    | |__/ || | \\_/ ||  /___//   | \\_/ ||  | . \\  
    |_____//   \____//   `__ `     \____//   |_|\_\\ 
     -----`     `---`    /_//       `---`    `-` --` 
                         `-`                         
    
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  • 16. Percent of Days within 1 Standard Deviation for Numbers of Hotel Rooms Occupied

    The histogram shows the distribution of the numbers of hotel rooms occupied for 150 days in a year. What percent of the days lie within 1 standard deviation of the mean?

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     _____      _____              _    _    _    _   
    |  __ \\   |  ___||     ___   | || | || | \  / || 
    | |  \ ||  | ||__      /   || | || | || |  \/  || 
    | |__/ ||  | ||__     | [] || | \\_/ || | .  . || 
    |_____//   |_____||    \__ ||  \____//  |_|\/|_|| 
     -----`    `-----`      -|_||   `---`   `-`  `-`  
                             `-`                      
    
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  • 17. Percent of Days within 2 Standard Deviations for Numbers of Hotel Rooms Occupied

    The histogram shows the distribution of the numbers of hotel rooms occupied for 150 days in a year. What percent of the days lie within 2 standard deviations of the mean?

    • Worked-Out Solution

      The mean is 125 hotel rooms occupied and the standard deviation is 44 hotel rooms occupied. Data values that lie within 2 standard deviations lie within the range 125 - 2(44) to 125 + 2(44), or 37 rooms to 213 rooms. Rounding to the nearest 10 gives a range of 40 to 210 rooms.

      Add the days with numbers of hotel rooms occupied within the range from 40 rooms to 210 rooms. The number of days with numbers of hotel rooms occupied within 2 standard deviations of the mean is

      Divide this number by the total number of days.

      So, about 92% of the days have numbers of rooms occupied that lie within 2 standard deviations of the mean.

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     _    _      ___     _    _      ___      _____   
    | \  / ||   / _ \\  | |  | ||   / _ \\   /  ___|| 
    |  \/  ||  / //\ \\ | |/\| ||  | / \ || | // __   
    | .  . || |  ___  |||  /\  ||  | \_/ || | \\_\ || 
    |_|\/|_|| |_||  |_|||_// \_||   \___//   \____//  
    `-`  `-`  `-`   `-` `-`   `-`   `---`     `---`   
                                                      
    
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  • 18. Comparing Distributions with the Normal Distribution

    The histogram shows the distribution of the numbers of hotel rooms occupied for 150 days in a year. Compare the percents in Exercises 16 and 17 with the percents given by the normal distribution.

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     _    _     _____   __    __     ___      _  _   
    | || | ||  |  ___|| \ \\ / //   / _ \\   | \| || 
    | || | ||  | ||__    \ \/ //   / //\ \\  |  ' || 
    | \\_/ ||  | ||__     \  //   |  ___  || | .  || 
     \____//   |_____||    \//    |_||  |_|| |_|\_|| 
      `---`    `-----`      `     `-`   `-`  `-` -`  
                                                     
    
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  • 19. Hours of Television Watched by Men and Women

    The histograms show the distributions of samples of hours of television watched per day by men and women. What is the significance of the smaller standard deviation for women?

    • Worked-Out Solution

      The smaller standard deviation for women means that the distribution of data values for women has less dispersion than the distribution of data values for men. In other words, the hours of television watched in the distribution for women are more tightly clustered about the mean than the hours of television watched in the men's distribution.

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      ______     ___     __   __     ___              
     /_   _//   / _ \\   \ \\/ //   / _ \\      ___   
       | ||    | / \ ||   \   //   | / \ ||    /   || 
      _| ||    | \_/ ||   / . \\   | \_/ ||   | [] || 
     /__//      \___//   /_//\_\\   \___//     \__ || 
     `--`       `---`    `-`  --`   `---`       -|_|| 
                                                 `-`  
    
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  • 20. Estimating Percents from Histograms

    The histograms show the distributions of samples of hours of television watched per day by men and women. Estimate the percents of men and women that watch at least 4 hours of television per day.

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     _    _      ___      _  _    _    _   __    __  
    | |  | ||   / _ \\   | \| || | || | || \ \\ / // 
    | |/\| ||  | / \ ||  |  ' || | || | ||  \ \/ //  
    |  /\  ||  | \_/ ||  | .  || | \\_/ ||   \  //   
    |_// \_||   \___//   |_|\_||  \____//     \//    
    `-`   `-`   `---`    `-` -`    `---`       `     
                                                     
    
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