Question

use the information given in the table on the right to complete each of the following statements.

brenda is 50 inches tall. her z-score is 0.5.

zach has a z-score of -1.5. his height is 46 inches.

approximately % of 7-year-old children are taller than 51 inches.

Explanation:

Identify given parameters

Using the Z-Score Formula knowledge point

$$
LATEXBLOCK0
$$

Calculate Brenda's z-score

Using the Z-Score Formula knowledge point

$$ z = \frac{x - \mu}{\sigma} = \frac{50 - 49}{2} = 0.5 $$

Calculate Zach's height

Using the Z-Score Formula knowledge point

$$
LATEXBLOCK1
$$

Calculate percentage taller than 51 inches

Using the Empirical Rule and Z-Score Formula knowledge points

$$
LATEXBLOCK2
$$

Answer:

Use the information given in the table on the right to complete each of the following statements.

Brenda is 50 inches tall. Her z-score is <blank>0.5</blank>.

Zach has a z-score of \(-1.5\). His height is <blank>46</blank> inches.

Approximately <blank>16</blank>% of 7-year-old children are taller than 51 inches.