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Section4.3Chapter 4 Exercises

  1. Cumulative SAT scores are normally distribute with mean 1100 and standard deviation 200. Use this information to sketch a diagram and answer each of the questions below.

    1. Approximately what percent of SAT scores are between 700 and 1500?
    2. What percent of SAT scores are less than or equal to 1500? What percent of the scores are greater than 1500?
    3. The scores of 68% of test takers are expected to be between what two values?
    4. What percent of SAT scores are between 1100 and 1300?
    5. The top 2.5% of the students will have a score greater than what value?
    6. What is the probability that a randomly selected student has an SAT score greater than 1300?
    7. What percent of SAT scores are 500 or less?
    8. What is the probability that a randomly selected student has an SAT score between 900 and 1500?
    9. What is the probability that a randomly selected student has an SAT score between 1300 and 1700?

  2. Suppose 460 high school seniors in a particular school district took the SAT exam.

    1. Approximately how many of the seniors in the district are expected to earn scores between 900 and 1500?
    2. Approximately how many of these students are expected to earn scores greater than 1300?
    3. Approximately 320 of the students are expected to earn a minimum score of what value?
    4. Approximately how many of the students are expected to earn scores higher than 1700?
    5. Approximately how many of the students are expected to earn scores between 700 and 1300?

  3. Recall that the heights of individuals are normally distributed. Women have an average height of 65 inches with a standard deviation of 3.5 inches.

    1. Suppose we randomly select 25 female UNL students. What is the standard deviation of the possible sample means? What is the probability that the average height of these women is between 64.3 and 65.7 inches?
    2. What if we select 100 random female students at UNL. What is the probability that the average height of these women is between 64.3 and 65.7 inches?
    3. What if we select 225 random female students at UNL. What is the probability that the average height of these women is between 64.3 and 65.7 inches?
    4. What if we select 2000 random female students at UNL. What is the probability that the average height of these women is between 64.3 and 65.7 inches?
    5. Suppose your Math 203 class is given a very small budget and asked to use it to estimate the average height of undergraduate women attending UNL. Since it is expensive to conduct large randomized surveys, the students in the class decide to ask approximately 200 female students their height and calculate the average. A student on campus who has not taken Math 203 finds out the survey only included 200 women and declares that since there are roughly 10,000 female undergraduate students at UNL, the results are probably wrong. What is an appropriate response to this criticism?
  4. Suppose 60% of voters favor candidate A over candidate B. Determine the standard deviation and 95% confidence interval for a polling sample of 1000 individuals.

  5. Suppose 52% of voters favor candidate A over candidate B.

    1. Determine the standard deviation and 95% confidence interval for a polling sample of 1000 individuals.
    2. Find the probability that the poll will predict a majority in favor of candidate B.
    3. Explain why the size of the actual voting population does not need to be given in this problem.