MATH 302 MATH302 MIDTERM Answers (APUS)

MATH 302 MATH302 MIDTERM Answers (APUS)

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MATH 302 MATH/302 MATH302 MIDTERM EXAM  (APUS)

    1. Which measure of central location is meaningful when the data are categorical?
    2. What type of probability uses sample spaces to determine the numerical probability that an event will occur?
    3. The formal way to revise probabilities based on new information is to use:
    4. 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 fewer than 40 batteries will last at least 8 hours?
  • Find the variance of the following probability distribution.
  • X
  • P(X)
  • 1
  • 0.20
  • 2
  • 0.15
  • 3
  • 0.25
  • 4
  • 0.25
  • 5
  • 0.15
    1. Which term is NOT synonymous with the expected value of a discrete probability distribution?
    2. Given that Z is a standard normal random variable, P(-1.0 < Z < 1.5) is
    3. The continuous distribution characterized by a symmetric, bell-shaped curve is the:
    4. The standard deviation of a probability distribution must be:
    5. Given that Z is a standard normal variable, the value z for which P(Z < z) = 0.2580 is
    6. The standard normal distribution has a mean of ___ and standard deviation of ___, respectively.
    7. One reason for standardizing random variables is to measure variables with:
    8. 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 variance of the data. Place your answer, rounded to two decimal places, in the blank. For example, 3.45 would be a legitimate entry
  • 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.

    Find the mean of the following probability distribution.
  • X
  • 1
  • 2
  • 3
  • 4
  • 5
  • P(X)
  • 0.20
  • 0.10
  • 0.35
  • 0.05
  • 0.30

  • Round your answer to two decimal place as necessary. For example, 4.56 would be a legitimate entry.
     
  • 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 were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.
     
  • x
  • 0
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  •  P (X=x)
  • 0.55
  • 0.15
  • 0.10
  • 0.10
  • 0.04
  • 0.03
  • 0.03

  • Find P(1 < X < 5).  Place your answer, rounded to two decimal places in the blank.  For example, 0.56 would be a legitimate entry
  • 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.
    An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:
    = chocolate chosen
    = strawberry chosen
    = vanilla chosen
    = ice cream on a cone
    ice cream in a cup

    Find the probability that the ice cream was sold in a cup and was strawberry flavor. Place your answer, rounded to 2 decimal places, in the blank. For exampe, 0.34 would be a legitimate entry.
    1. 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 reading list for a course contains 20 articles. How many ways are there to choose three articles from this list? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entr
    2. 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.
    3. 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 mean 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, 123 would be a legitimate entry
    4. 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
    5. 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 Wendy’s fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday, the demand for hamburgers is normally distributed with a mean of 450 and standard deviation of 80 and the demand for chicken sandwiches is normally distributed with a mean of 120 and standard deviation of 30.

      How many chicken sandwiches must the restaurant stock to be 99% sure of not running out on a given day? Place you answer, rounded to the nearest whole number in the blank. For example, 345 would be a legitimate entry
  • 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 mean weight of loads of coal placed in train cars by a loading machine is 43.0 tons with a standard deviation of 8.0 tons. Assuming that the weight of loads placed in the train cars by this loader are normally distributed, if a random sample of 9 loads is chosen for a weight check, find the probability that the mean weight of those loads is more than 40.60 tons.
     
    Place your answer, rounded to four decimal places, in the blank
  1. 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.
  2. Using the standard normal curve, the Z- score representing the 85th percentile is 0.67
  3. The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.

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