Question

introduction to normal distributions
instruction active
try it calculate z - scores
jordan is 53 inches tall. what is his z - score?
jake is 44 inches tall. what is his z - score?
jacob is 49 inches tall. what is his z - score?
done

age	mean	standard deviation

$z = \frac{x - \mu}{\sigma}$

Explanation:

Step1: Calculate Jordan's z - score

We know the formula for z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For Jordan, $x = 53$, $\mu=49$, $\sigma = 2$.
Substitute the values into the formula: $z=\frac{53 - 49}{2}=\frac{4}{2}=2$.

Step2: Calculate Jake's z - score

For Jake, $x = 44$, $\mu = 49$, $\sigma=2$.
Substitute into the formula: $z=\frac{44 - 49}{2}=\frac{- 5}{2}=- 2.5$.

Step3: Calculate Jacob's z - score

For Jacob, $x = 49$, $\mu = 49$, $\sigma = 2$.
Substitute into the formula: $z=\frac{49 - 49}{2}=\frac{0}{2}=0$.

Answer:

Jordan's z - score: 2; Jake's z - score: - 2.5; Jacob's z - score: 0