MATH 302 MATH/302 MATH302 Midterm Solutions (APUS)

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MATH 302 Midterm Exam Answers (APUS)

  1. If you classified the fruit in a basket as apple, orange, or banana, this would be an example of which level of measurement?
  2. The result of tossing a coin once will be either head or tail. Let A and B be the events of observing head and tail, respectively. The events A and B are:
  3. If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then the probability that either A or B or both occur is:
  4. The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.
  5. Suppose that 50 identical batteries are being tested. After 8 hours of continuous use, assume that a given battery is still operating with a probability of 0.70 and has failed with a probability of 0.30.What is the probability that greater than 30 batteries will last at least 8 hours?
  6. If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game?
  7. If Z is a standard normal random variable, the area between z = 0.0 and z =1.30 is 0.4032, while the area between z = 0.0 and z = 1.50 is 0.4332. What is the area between z = -1.30 and z = 1.50?
  8. If Z is a standard normal random variable, then the value z for which P(-z < Z < z) equals 0.8764 is
  9. If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?
  10. The continuous distribution characterized by a symmetric, bell-shaped curve is the:
  11. Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 < X < 90) is
  12. The standard deviation of a probability distribution is a:
  13. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
    The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.

    Compute the standard deviation of the data. Place your answer, rounded to two decimal places, in the blank. For example, 3.45 would be a legitimate entry

  14. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question
  15. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation, 24% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.  
  16. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not. Mothers Against Drunk Driving (MADD) is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Five hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:
  17. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
    If you have six books, but there is room for only four books on the shelf, in how many ways can these books be arranged on the shelf? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry
  18. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
    Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

    Find the standard deviation of the sampling distribution of the means of average weekly earnings for samples of size 100. Place your answer in the blank. Do not include a dollar sign. For example, 7 would be a legitimate entry

  19. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
    A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8.

    What is the probability of getting a score of 68 or less on this exam? Place your answer, rounded to 4 decimal places in the blank. For example, 0.3456 would be a legitimate entry

  20. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
    Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

    Find the probability that the mean of the sample is greater than $460. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate answer.

  21. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
    Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam.

    What score represents the 70th percentile score on the mathematics exam? Place your answer in the blank, rounded to a whole number. For example, 62 would be a legitimate entry.

  22. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
    Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.

    Find probability that the mean of the sample is less than $445. Place your answer, rounded to 4 decimal places, in the blank. For example, 0.2345 would be a legitimate entry.

  23. Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), “E” or “e” (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
    Complex numbers should be in the form (a + bi) where “a” and “b” need to have explicitly stated values.
    For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.
    A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9.

    What is the probability that a randomly selected customer will spend between $20 and $35 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.

  24. Using the standard normal curve, the Z- score representing the 99th percentile is 2.326.
  25. The left half under the normal curve is slightly smaller than the right half.