Question

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.

Answer 1

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.

Answer 2

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