Question

1. find the z - score for the data point x given mean μ and standard deviation σ. round to two decimal places as needed.

x = 78
μ = 75
σ = 2

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Substitute the given values

We are given that $x = 79$, $\mu=75$, and $\sigma = 2$. Substitute these values into the formula:
$z=\frac{79 - 75}{2}$

Step3: Simplify the numerator

First, calculate the numerator: $79-75 = 4$.

Step4: Divide to find z - score

Then, divide the numerator by the denominator: $z=\frac{4}{2}=2.00$

Answer:

2.00