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If a distribution of test scores is normal with a mean of 78 and a standard deviation of 11, calculate the z-score for the following scores X Z-score 60 70 80 90 60 65 70 80 99 89 75 Make sure to round up your answers to two digits after the decimal point.

2 Answers

5 votes

Final answer:

To calculate the z-score, subtract the mean from the score and divide by the standard deviation. The calculated z-scores for the given test scores are -1.64, -0.73, 0.18, 1.09, -1.64, -1.18, -0.73, 0.18, 1.91, 1.00, and -0.27.

Step-by-step explanation:

The z-score is a standardized value that measures how many standard deviations a score is above or below the mean. To calculate the z-score, we use the formula z = (X - µ) / σ, where X is the score, µ is the mean, and σ is the standard deviation.

  1. For the score 60, the z-score is (60 - 78) / 11 = -1.64.
  2. For the score 70, the z-score is (70 - 78) / 11 = -0.73.
  3. For the score 80, the z-score is (80 - 78) / 11 = 0.18.
  4. For the score 90, the z-score is (90 - 78) / 11 = 1.09.
  5. For the score 60, the z-score is (60 - 78) / 11 = -1.64.
  6. For the score 65, the z-score is (65 - 78) / 11 = -1.18.
  7. For the score 70, the z-score is (70 - 78) / 11 = -0.73.
  8. For the score 80, the z-score is (80 - 78) / 11 = 0.18.
  9. For the score 99, the z-score is (99 - 78) / 11 = 1.91.
  10. For the score 89, the z-score is (89 - 78) / 11 = 1.00.
  11. For the score 75, the z-score is (75 - 78) / 11 = -0.27.

User Kelly Nicholes
by
8.0k points
1 vote

Answer:

Step-by-step explanation:

As we know z- score is defined by the formula
z=(x-\mu )/(\sigma )

Mean of the scores is given as 78 and standard deviation 11.

Now for x = 60


z=(x-\mu )/(\sigma )


z=(60-78)/(11)=((-18))/(11)=-1.64

For x = 70


z=(70-78)/(11)


z=((-8))/(11) =-0.73

For x = 80


z=(80-78)/(11)

z = 0.18

For x = 90


z=(90-78)/(11)

z = 1.09

For x = 60

z = -1.64

For x = 65


z=(65-78)/(11)

z = -1.18

For x = 70

z = -0.73

For x = 80

z = 0.18

For x = 99


z=(99-78)/(11)

z = 1.91

For x = 89


z=(89-78)/(11)

z = 1

For x = 75


z=(75-78)/(11)

z = -0.27

User Lorna
by
8.7k points

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