Percentages

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A data set is normally distributed with the *mean* value $\mu = 77.00$ and *standard deviation* $\sigma = 15.00$. What percentage of data values are less than $x = 54.00$

**Answer**

*z-score* of $x=54.00 = z = \frac{x-\mu}{\sigma} = \frac{54.00 - 77.00}{15.00}=-1.53$

The area under the *standard normal distribution curve* to the left of $z=-1.53$ is $0.0630$

The percentage of data values that are less than $x=54.00$ is $6.30$