Use the empirical rule to determine the approximate probability that a z value is between 0 and 1 on the standard normal curve.

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Use the empirical rule to determine the approximate probability that a z value is between 0 and 1 on the standard normal curve.

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Answer 1 · 2015-02-20T18:15:12

You need to use a table of standar normal distribution curve. There are different kind of tables (cumulative, fi function, stc..), but your anwer is:
$P (0 < z < 1) = 0.34$ $P( 0 < z < 1) = 0.34$

The empirical rule allows you to make a quick assessment of probability without using a table. Just memorise these three numbers:

$0.34 = 34 %$ $0.34=34%$ is less than one standard deviation $σ$ $sigma$ higher than the mean $μ$ $mu$
$0.135 = 13.5$ $0.135=13.5$ is between $σ$ $sigma$ and $2 σ$ $2sigma$ higher than $μ$ $mu$
$0.025 = 2.5 %$ $0.025=2.5%$ is more than $2 σ$ $2sigma$ higher than $μ$ $mu$

The same goes for values below $μ$ $mu$ , as the normal curve is symmetrical. (So you have 68% of your values between $μ - σ$ $mu-sigma$ and $μ + σ$ $mu+sigma$ , or between $z = - 1$ $z=-1$ and $z = + 1$ $z=+1$ )

Remember every $σ$ $sigma$ translates to $1$ $1$ on the $z$ $z$ -scale

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Use the empirical rule to determine the approximate probability that a z value is between 0 and 1 on the standard normal curve.

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