Questions: A normal distribution has a mean of 148 and a standard deviation of 7. Find the z-score for a data value of 131. Round to two decimal places

Transcript text: A normal distribution has a mean of 148 and a standard deviation of 7 . Find the $z$-score for a data value of 131. $\square$ Round to two decimal places

Solution

Solution Steps

Step 1: Calculate the Z-Score

To find the $ z $-score for a data value of $ X = 131 $ in a normal distribution with mean $ \mu = 148 $ and standard deviation $ \sigma = 7 $, we use the formula:

\[ z = \frac{X - \mu}{\sigma} \]

Substituting the values:

\[ z = \frac{131 - 148}{7} = \frac{-17}{7} \approx -2.4286 \]

Rounding to two decimal places, we have:

\[ z \approx -2.43 \]