use the information given in the table on the right to complete each of the following statements. brenda is…
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.
Answer
Explanation:
Step1: Calculate z - score for 51 inches
The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $\mu = 49$ inches, $\sigma=2$ inches, and $x = 51$ inches. Then $z=\frac{51 - 49}{2}=\frac{2}{2}=1$.
Step2: Use the standard normal distribution
In a standard normal distribution, the proportion of data to the right of $z = 1$ can be found using the property that the total area under the curve is 1. The area to the left of $z = 1$ is approximately 0.8413 (from standard normal tables or knowledge of the empirical rule). So the area to the right of $z = 1$ is $1-0.8413 = 0.1587$.
Step3: Convert to percentage
To convert the proportion to a percentage, we multiply by 100. So $0.1587\times100 = 15.87\approx16$.
Answer:
16