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Complete the statement. Round your answer to the nearest thousandth. $\newline$ In a population that is normally distributed with mean $19$ and standard deviation $19$ , the bottom $20\%$ of the values are those less than ___.

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Find values of normal variables

Full solution

Q. Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

19

and standard deviation

19

, the bottom

20\%

of the values are those less than ___.

Find z-score for $20$ \%: Find the z-score for $20$ \%. Using a z-table or calculator, the z-score for $20$ \% is approximately $-0.842$ .
Use z-score formula: Use the z-score formula to solve for $X$ .
mean ( $\mu$ ): $19$
standard deviation ( $\sigma$ ): $19$
z-score ( $Z$ ): $-0.842$
$Z = \frac{X - \mu}{\sigma}$
$-0.842 = \frac{X - 19}{19}$
Multiply to isolate $X$ : Multiply both sides by the standard deviation to isolate $X - \mu$ . $-0.842 \times 19 = X - 19$ $-16.0 = X - 19$

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