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

Answer:

Benjamin and Cynthia will have positive z-scores

Cynthia’s z-score is: 0.2

Step-by-step 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:

$Z = \frac{x- \mu}{\sigma}$.

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

$Z = \frac{55-70}{10}$

$Z = -1.5$

Benjamin, completed the exam in 86 minutes

$x = 86$

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

$Z =\frac{86-70}{10}$

$Z = 1.6$

Cynthia, completed the exam in 72 minutes

$x = 72$

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

$Z = \frac{72-70}{10}$

$Z = 0.2$

Benjamin and Cynthia will have positive z-scores

Answer 2

Answer:

Benjamin and Cynthia will have positive z-scores

Cynthia’s z-score is: 0.2