find individual values in normal distributions\nuse the information given in the table on the right to…
find individual values in normal distributions\nuse the information given in the table on the right to complete each of the following statements.\nbrenda is 50 inches tall. her z - score is 0.5\ncomplete\nzach has a z - score of - 1.5. his height is 46 inches.\ncomplete\napproximately % of 7 - year - old children are taller than 51 inches.\ndone
Answer
Explanation:
Step1: Calculate the 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. $z=\frac{51 - 49}{2}=\frac{2}{2}=1$
Step2: Use the standard normal distribution table
The standard - normal distribution table gives the cumulative probability $P(Z\leq z)$. For $z = 1$, from the standard - normal table, $P(Z\leq1)=0.8413$. The proportion of values greater than $z = 1$ is $P(Z>1)=1 - P(Z\leq1)$. $P(Z>1)=1 - 0.8413 = 0.1587$
Step3: Convert to percentage
To convert the proportion to a percentage, multiply by 100. $0.1587\times100 = 15.87\approx16$
Answer:
16