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Common Core Standard HSS-ID.A.4 Questions

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

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Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
Which of the following best defines a standard normal distribution?
  1. A normal distribution with [math]mu = 0[/math] and [math]sigma =1[/math].
  2. A normal distribution with [math]mu = 1[/math] and [math]sigma = 0[/math].
  3. A normal distribution with [math]mu=1[/math] and [math]sigma=1[/math].
  4. A normal distribution with [math]mu = 0[/math] and [math]sigma = 0[/math].
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
Which of the following is true about the mean, median, and mode of a normal distribution?
  1. They are all equal.
  2. The mean and median are always equal, but the mode is either greater or less than them.
  3. The mode and median are always equal, but the mean is usually less than them.
  4. They may or may not be equal; there is no general rule.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
What does a z-score indicate about a given data point (or raw score) from a normal distribution?
  1. The probability that the data point will occur.
  2. The percentile in which the data point lies.
  3. The number of standard deviations away from the mean the data point lies.
  4. The frequency of the data point.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
Which parameters are needed to define a normal distribution?
  1. The mean and the standard deviation.
  2. The mean alone.
  3. The range and the mean.
  4. The range, standard deviation, and IQR.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
Which of the following is/are true for the standard normal distribution? Choose all correct answers.
  1. 34% of the values are between 0 and 1.
  2. 95% of the values are between -2 and 2.
  3. About 50% of the values are less than 6.
  4. About 100% of the values are greater than -7.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
The graph of a normal distribution is plotted. However, the standard deviation used was incorrect. The actual standard deviation is larger than what was used. What will happen to the shape of the graph?
  1. It will become narrower and taller.
  2. It will become wider and shorter.
  3. It will become wider and taller.
  4. It will become narrower and shorter.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
Which of the following best defines a z-table?
  1. A table which gives the probabilities of various z-scores occurring.
  2. A table which gives the probabilities of various z-scores being less than or greater than the mean.
  3. A table which gives the percentage of values within one standard deviation of a certain z-score.
  4. A table which gives the percentage of values between 0 (or positive/negative infinity) and a certain z-score.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
Which of the following is true about calculating a z-score for data which is not normally distributed?
  1. There is no difference from normally distributed data.
  2. Although it can be computed, it may not have a typical (or any useful) meaning.
  3. It can be computed, but the formula is slightly different (one takes the square root of the usual z-score).
  4. It is impossible to compute the z-score for non-normally distributed data.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.4
Which of the following is true concerning z-scores?
  1. Z-scores are always positive.
  2. Z-scores are negative only when the population mean is negative.
  3. Z-scores are positive if the mean is less than the raw score, and negative if the mean is greater than the raw score.
  4. Z-scores are positive if the standard deviation is greater than the raw score, and negative if the standard deviation is less than the raw score.
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