Albarellak

2021-01-08

Find the following probabilities for the standard normal distribution  $Pr\left(z>2.5\right)$

joshyoung05M

Expert

$z=\frac{x-\mu }{\sigma }$
The normal distribution is symmetric about mean 0.5.
$P\left(z>2.5\right)=0.5-Pr\left(z\le 2.5\right)$
The probability that the z lies between 0 and 2.5 is equal to the area that lies under the curve from 0 and 2.5.
In the column headed by A across 2.5 the corresponding value is 0.4938.
The probability $P\left(0\le z\le 2.5\right)$ is ${A}_{2.5}$.
So the value of ${A}_{2.5}$ from the appendix C is 0.4938.

The value of $P\left(z>2.5\right)$
$P\left(z>2.5\right)=0.5—0.4938=0.0062$

Aswer is 0.0062.

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