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Statistics

  1. Solve each percentage question. (6 points)
    1. What is 60% of 45?
    2. What is 24% of 75?
    3. 3 is 15% of what number?
    4. 40 is 125% of what number?
    5. 19 is what percent of 20?
    6. 63 is what percent of 175?

  2. Figure out the percent increase or percent decrease. (8 points)
    1. From 20 to 30
    2. From 60 to 36
    3. From 7 to 63
    4. From 200 to 138

  3. Find the mean, median, mode, and range given: (9 points)
    1. the numbers 5, 2, and 5.
    2. the exam scores 90, 72, 85, 60, 99, 60 and 94.
    3. the ages 35, 3, 10, 52, 17, 85, 16, 10, 35, and 7.

  4. Find the original numbers. (9 points)

    1. Three numbers that have mean 8, median 10, no mode, and range 8.
    2. Five numbers that have mean 10, median 10, mode 1, and range 19.
    3. Six numbers that have mean 1, median 1/2, mode 0, and range 4.

  5. Twenty Citrus College students were surveyed to find out the number of miles they commute to get to school. (20 points)

    2  7  16  11  18   6  3  4  12  8  7  15  5  10  8  12  15  8  9  4

    1. Construct a frequency disribution for the data using 6 classes.
    2. Draw a histogram to give a graphic representation of the data.
    3. Compute the mean distance traveled.
    4. Compute the standard deviation of the distances.

  6. Final Average
    In a certain class, homework counts as 50% of the grade, two mid-semester exams are worth 15% each, and the final exam is worth 20%. If your homework average is 97 and your exam scores are 68, 79, and 76 respectively, what will be your final average? (6 points)

  7. The Better Test
    A student scored 65 on a calculus test that had a mean of 50 and a standard deviation of 10. She scored 50 on a history test with a mean of 40 and a standard deviation of 5. On which test did she perform better? Show this using a bell curve. (6 points)

  8. TV Raffle
    One thousand tickets are sold at $1 each. The winning ticket holder will receive a TV valued at $350. What is the expected gain for a person that purchases one ticket? (6 points)

  9. Gambler's Prediction
    If you bet $100 on a single number in Roulette, what is your expected gain? (There are 38 spaces on the wheel, and winning number earns a payoff of $35 for every dollar bet.) (6 points)

  10. Looking For A Job
    Thirty-six employed Los Angeles County residents are surveyed. Each is asked how long it took him or her to find employment. The responses have a mean of 5.9 months and a standard deviation of 0.8 months. Use this data to find a 95% confidence interval of the average time needed for a Los Angeles County resident to find a job. (6 points)

  11. Telling The "Truth"
    Suppose you served as a publicity worker for the Bush administration and your job was to portray George in as positive a light as possible without technically lying. Draw a graph about the unemployment rate that will do this. (Not taken from actual unemployment records.) (6 points)

      Time Period Unemployment Time Period Unemployment
      Fall 2004   6% Fall 2005   5½%
      Winter 2005   6½% Winter 2006   6%
      Spring 2005   6% Spring 2006   6%
      Summer 2005   5% Summer 2006   7%

  12. Restaurant Arrival
    Two people arrive at a restaurant independently. Each arrives at a random time uniformly distributed between 5 p.m. and 6 p.m. What is the probability they arrive within 10 minutes of each other? (12 points)
 
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