Question

Use the information on the right to determine which students will have positive z-scores.

A) Aaliyah, who completed the exam in 55 minutes
B) Benjamin, who completed the exam in 86 minutes
C) Cynthia, who completed the exam in 72 minutes

Cynthia’s z-score is: ???

Answer 1

Benjamin and Cynthia will have positive z-scores

Cynthia’s z-score is: 0.2

Answer 2

Benjamin and Cynthia will have positive z-scores

Cynthia’s z-score is: 0.2

Explanation:

The z-scores give us information about how many standard deviations from the mean a data is found. This difference can be negative, if the data is n deviations to the left of the mean, or it can be positive if the data is n deviations to the right of the mean.

To calculate the Z scores we calculate the difference between the value of the data and the mean and then we divide this difference between the standard deviation.

Thus:

`Z = (x- \mu)/(\sigma)`.

Where x is the value of the data, μ is the mean and σ is the standard deviation

`\mu = 70\ minutes`

`\sigma = 10\ minutes`

Aaliyah, completed the exam in 55 minutes.

So

`x = 55`

`55 <70` then the z score will be negative

`Z = (55-70)/(10)`

`Z = -1.5`

Benjamin, completed the exam in 86 minutes

`x = 86`

`86> 70` then the z score will be positive

`Z =(86-70)/(10)`

`Z = 1.6`

Cynthia, completed the exam in 72 minutes

`x = 72`

`72> 70` then the z score will be positive

`Z = (72-70)/(10)`

`Z = 0.2`

Benjamin and Cynthia will have positive z-scores