Percentages

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A data set is normally distributed with the *mean* value $\mu = 65.00$ and *standard deviation* $\sigma = 14.00$. What percentage of data values are less than $x = 45.00$

**Answer**

*z-score* of $x=45.00 = z = \frac{x-\mu}{\sigma} = \frac{45.00 - 65.00}{14.00}=-1.43$

The area under the *standard normal distribution curve* to the left of $z=-1.43$ is $0.0764$

The percentage of data values that are less than $x=45.00$ is $7.64$