Questions: Consider a set of data in which the sample mean is 49.6 and the sample standard deviation is 6. Calculate the z-score given that x=48.2. Round your answer to two decimal places.

Consider a set of data in which the sample mean is 49.6 and the sample standard deviation is 6. Calculate the z-score given that x=48.2. Round your answer to two decimal places.

Transcript text: Consider a set of data in which the sample mean is 49.6 and the sample standard deviation is 6. Calculate the $z$-score given that $x=48.2$. Round your answer to two decimal places.

Solution

Solution Steps

To calculate the z-score, we use the formula: $ z = \frac{x - \mu}{\sigma} $, where $ x $ is the data point, $ \mu $ is the sample mean, and $ \sigma $ is the sample standard deviation. We will substitute the given values into this formula to find the z-score.

Step 1: Identify the Given Values

We are given the following values:

Sample mean ($\mu$) = 49.6
Sample standard deviation ($\sigma$) = 6
Data point ($x$) = 48.2

Step 2: Apply the Z-Score Formula

The formula for calculating the z-score is: \[ z = \frac{x - \mu}{\sigma} \] Substituting the given values into the formula, we have: \[ z = \frac{48.2 - 49.6}{6} \]

Step 3: Calculate the Z-Score

Perform the calculation: \[ z = \frac{-1.4}{6} = -0.2333 \]

Step 4: Round the Z-Score

Round the z-score to two decimal places: \[ z \approx -0.23 \]