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If the data set has a mean of 30 and a standard deviation of 10, what is the z-s

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Question: If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?

Options:

  1. 1
  2. 0
  3. 2
  4. -1

Correct Answer: 2

Solution: 

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.

If the data set has a mean of 30 and a standard deviation of 10, what is the z-s

Practice Questions

Q1
If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?
  1. 1
  2. 0
  3. 2
  4. -1

Questions & Step-by-Step Solutions

If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?
  • Step 1: Identify the mean of the data set, which is given as 30.
  • Step 2: Identify the standard deviation of the data set, which is given as 10.
  • Step 3: Identify the value for which you want to find the z-score, which is 40.
  • Step 4: Use the z-score formula: Z-score = (X - Mean) / Standard Deviation.
  • Step 5: Substitute the values into the formula: Z-score = (40 - 30) / 10.
  • Step 6: Calculate the difference: 40 - 30 = 10.
  • Step 7: Divide the difference by the standard deviation: 10 / 10 = 1.
  • Step 8: The z-score of the value 40 is 1.
  • Z-score – A z-score indicates how many standard deviations a data point is from the mean.
  • Mean – The average value of a data set, calculated by summing all values and dividing by the number of values.
  • Standard Deviation – A measure of the amount of variation or dispersion in a set of values.
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