Which of the following statements are TRUE about the normal distribution? Check all that apply.The area to the left of a z-score plus the area to the right of that same z-score will always equal 1.A data value with z-score = -1.5 is located 1.5 standard deviations below the mean.The Empirical Rule only applies when a value is exactly 1, 2, or 3 standard deviations away from the mean.The mean corresponds to the z-score of 1.A z-score is the number of standard deviations a specific data value is from the mean of the distribution.
Question
Which of the following statements are TRUE about the normal distribution? Check all that apply.The area to the left of a z-score plus the area to the right of that same z-score will always equal 1.A data value with z-score = -1.5 is located 1.5 standard deviations below the mean.The Empirical Rule only applies when a value is exactly 1, 2, or 3 standard deviations away from the mean.The mean corresponds to the z-score of 1.A z-score is the number of standard deviations a specific data value is from the mean of the distribution.
Solution
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True. The area under the curve of a normal distribution equals 1. Therefore, the area to the left of a z-score plus the area to the right of that same z-score will always equal 1.
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True. A z-score of -1.5 means that the data value is 1.5 standard deviations below the mean.
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False. The Empirical Rule, also known as the 68-95-99.7 rule, applies to any data set that follows a normal distribution, not just values that are exactly 1, 2, or 3 standard deviations away from the mean.
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False. The mean, median, and mode of a normal distribution all correspond to a z-score of 0, not 1.
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True. A z-score is indeed the number of standard deviations a specific data value is from the mean of the distribution.
Similar Questions
Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is false about the z value corresponding to a given x value?Multiple ChoiceA positive z = (x − μ)/σ indicates how many standard deviations x is above μ.The z value corresponding to x = μ is zero.The z value corresponding to a given value of x assumes any value between 0 and 1.A negative z = (x − μ)/σ indicates how many standard deviations x is below μ.
Based on what you have studied in this unit, reflect and answer the following questions:What are the main characteristics of the normal distribution?Why is it advantageous to use the Z scores?For a standard normal distribution, about 68% of values falls within one standard deviation of the mean; about 95% falls within two standard deviations; and about 99.7% falls within three standard deviations. Suppose the distribution of math scores in the SAT follow a normal distribution with a mean µ=700 and a standard deviation σ=150.Calculate the Z-score for an SAT Math score of 600. Interpret it in your own word.Find the interval [a, b] that captures 68% of the SAT Math score in this example.Find the interval [a, b] that captures 95% of the SAT Math score in this example.Find the interval [a, b] that captures 99.7% of the SAT Math score in this example.
Which of the following about the normal distribution is NOT true?
In the z-score formula, which of the following is true if the value in the numerator is a negative value?Group of answer choicesthat the xi value lies to the left of the meanthat the mean is of lesser value than the xi valuethat the mean is of negative valuethat the numerator value cannot be divided by the standard deviation
In a standard normal distribution, what is the Z-score of the mean? 0 1 -1 It varies
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