Probability And Statistics Midterm Review

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Probability And Statistics Midterm Review - Quiz

Questions and Answers
  • 1. 

    If I collect data from the entire population, I've performed a__________________

    • A.

      Sample

    • B.

      Survey

    • C.

      Census

    • D.

      Proportion

    Correct Answer
    C. Census
    Explanation
    If I collect data from the entire population, I've performed a census. A census is a method of data collection where information is gathered from every individual or unit in a population. It provides a comprehensive and accurate representation of the entire population, unlike a sample or survey which only collects data from a subset of the population. A census is typically used to gather demographic, social, and economic information for government purposes or research studies.

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  • 2. 

    The following are examples of discrete data (Check all that apply.)

    • A.

      Number of brown M&Ms in a bag

    • B.

      Weight of a bag of M&Ms

    • C.

      Favorite M&M color

    • D.

      Number of stores that sell M&Ms

    Correct Answer(s)
    A. Number of brown M&Ms in a bag
    C. Favorite M&M color
    D. Number of stores that sell M&Ms
    Explanation
    Discrete data refers to data that can only take on specific values and cannot be measured on a continuous scale. In this case, the number of brown M&Ms in a bag, favorite M&M color, and number of stores that sell M&Ms are all examples of discrete data. These variables can only take on specific whole number values, such as 0, 1, 2, etc. On the other hand, the weight of a bag of M&Ms is an example of continuous data, as it can take on any value within a certain range and can be measured on a continuous scale.

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  • 3. 

    If you collect data on cars by sampling cars in the nearest parking lot, you have performed a.... 

    • A.

      Clustered sample

    • B.

      Convenience sample

    • C.

      Stratified sample

    • D.

      Random sample

    • E.

      Self-selected sample

    Correct Answer
    B. Convenience sample
    Explanation
    A convenience sample is a type of sampling method where the researcher selects the easiest or most readily available individuals or objects to include in the study. In this case, if you collect data on cars by sampling cars in the nearest parking lot, you have performed a convenience sample because you are selecting cars based on their proximity and convenience rather than using a random or systematic method.

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  • 4. 

    What are the measures of variation? (Check all that apply.)

    • A.

      Median

    • B.

      Range

    • C.

      Standard deviation

    • D.

      Z-score

    Correct Answer(s)
    B. Range
    C. Standard deviation
    Explanation
    The measures of variation refer to the statistical tools used to understand the spread or dispersion of data. The range is a measure that calculates the difference between the highest and lowest values in a dataset, providing an indication of how spread out the data points are. Standard deviation is another measure of variation that quantifies the average amount of deviation or dispersion from the mean in a dataset. Therefore, the correct answer includes both the range and standard deviation as measures of variation.

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  • 5. 

    Number of ways to roll a seven with two dice.

    Correct Answer(s)
    6
    Explanation
    When rolling two dice, there are a total of 36 possible outcomes (6 outcomes for the first dice multiplied by 6 outcomes for the second dice). To roll a seven, we need to find the combinations where the sum of the two dice is equal to seven. There are six possible combinations: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Therefore, the number of ways to roll a seven with two dice is 6.

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  • 6. 

    Which of the following measurements are part of a box plot (box and whisker diagram)

    • A.

      Upper quartile

    • B.

      Variance

    • C.

      Mean

    • D.

      Z-score

    Correct Answer
    A. Upper quartile
    Explanation
    A box plot, also known as a box and whisker diagram, displays the distribution of a dataset by showing the minimum, maximum, median, lower quartile, and upper quartile. The upper quartile is the value that separates the upper 25% of the data from the lower 75%. It is represented by the top boundary of the box in the box plot. Variance, mean, and z-score are not part of a box plot as they represent different statistical measures.

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  • 7. 

    To find the probability of a single value in a normal distribution, use the following calculator function:

    Correct Answer
    normalpdf, normpdf
    Explanation
    The answer is "normalpdf, normpdf" because these are the calculator functions used to find the probability of a single value in a normal distribution. These functions calculate the probability density function (PDF) of the normal distribution at a given point. By inputting the appropriate values such as the mean and standard deviation, these functions can provide the probability of a specific value occurring in a normal distribution.

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  • 8. 

    This calculation uses the mean and standard deviation to normalize a value.

    • A.

      Mean

    • B.

      Z-score

    • C.

      Permutation

    • D.

      Combination

    Correct Answer
    B. Z-score
    Explanation
    The z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and dividing the result by the standard deviation. The z-score allows for the normalization of values, making it easier to compare and analyze data. In this case, the calculation mentioned in the question is using the mean and standard deviation to normalize a value, which is why the correct answer is the z-score.

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  • 9. 

    Phone number is an example of a permutation

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    A phone number can be considered as an example of a permutation because it is a unique arrangement of digits that can be used to identify a specific telephone line. Each digit in the phone number holds a specific place value, and the order of the digits is important in determining the correct number. Therefore, a phone number can be seen as a permutation of digits.

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  • 10. 

    What is the following calculation?    

    Correct Answer
    z-score, Z-score, zscore, Zscore, z score, Z score
    Explanation
    The given answer refers to the various ways of representing the statistical term "z-score". A z-score is a measure of how many standard deviations an individual data point is from the mean of a distribution. It is used to standardize and compare data points from different distributions. The different variations in the answer represent different ways of writing and referring to the same concept.

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  • 11. 

    What is the following calculation?

    Correct Answer
    permutation, Permutation
  • 12. 

    What is the following calculation? 

    Correct Answer
    Combination, combination
  • 13. 

    If you've sellected several schools at random and them sample every car in their parking lots you have performed a...

    • A.

      Clustered sample

    • B.

      Convenience sample

    • C.

      Stratified sample

    • D.

      Random sample

    • E.

      Self-selected sample

    Correct Answer
    A. Clustered sample
    Explanation
    A clustered sample refers to selecting groups or clusters from a population rather than individual elements. In this scenario, the individual schools can be considered as clusters, and by randomly selecting several schools and sampling every car in their parking lots, a clustered sample is being performed. This method allows for a more efficient and practical way of sampling when the population is large and spread out.

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  • 14. 

    True or false: 

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    The correct answer is "True". This means that the statement being asked about is true or accurate.

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  • 15. 

    Votes in an election is what kind of measurement?

    • A.

      Nominal

    • B.

      Ordinal

    • C.

      Interval

    • D.

      Ratio

    Correct Answer
    D. Ratio
    Explanation
    In an election, votes can be counted and measured on a numerical scale. They have a meaningful zero point and can be compared and analyzed using mathematical operations such as addition, subtraction, multiplication, and division. Therefore, votes in an election are considered a ratio measurement.

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  • 16. 

    If the probability of a late arrival is 20%, I can expect 6 late arrivals out of 30 flights

    • A.

      True

    • B.

      False

    Correct Answer
    A. True
    Explanation
    Based on the given information, it states that the probability of a late arrival is 20%. This means that out of every 100 flights, 20 flights are expected to be late. Therefore, if we consider 30 flights, we can expect approximately 20% of 30, which is 6, to be late arrivals. Hence, the statement is true.

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  • 17. 

    In a normally distributed set of data, the probability that a value is within one standard deviatio of the mean is 

    • A.

      50%

    • B.

      5%

    • C.

      34%

    • D.

      68%

    • E.

      17.5%

    Correct Answer
    D. 68%
    Explanation
    In a normally distributed set of data, approximately 68% of the values fall within one standard deviation of the mean. This is because the normal distribution is symmetric and bell-shaped, with the mean at the center. The standard deviation measures the spread of the data around the mean. By the empirical rule or the 68-95-99.7 rule, about 68% of the data falls within one standard deviation of the mean.

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  • 18. 

    The median is the preferred measure of center for nominal data

    • A.

      True

    • B.

      False

    Correct Answer
    B. False
    Explanation
    The statement that the median is the preferred measure of center for nominal data is false. The median is commonly used for ordinal and interval/ratio data, where the values have a natural order and can be ranked. However, for nominal data, which consists of categories or groups with no inherent order, the mode is typically the preferred measure of center. The mode represents the most frequently occurring category or group in the data, making it more suitable for nominal data.

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  • 19. 

    The opposite of "at least 10" is

    Correct Answer
    at most 9, At most 9, at most nine, At most nine
    Explanation
    The opposite of "at least 10" means a number that is less than or equal to 9. Therefore, the correct answer is "at most 9, At most 9, at most nine, At most nine."

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  • 20. 

    In a uniform distribution, the probability any any value is the

    Correct Answer
    same, Same, equal, Equal
    Explanation
    In a uniform distribution, all values have an equal probability of occurring. This means that the probability of any value is the same as the probability of any other value in the distribution. Therefore, the statement "same, same, equal, equal" accurately describes the concept of a uniform distribution.

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