# A population of values has a normal distribution with \mu = 49 and \sigma = 79.5. You intend to draw a random sample of size n=84. Find the probability that a single randomly selected value is greater than 72.4. P(X>72.4)=? Write your answers as numbers accurate to 4 decimal places.

A population of values has a normal distribution with $\mu =49$ and $\sigma =79.5$. You intend to draw a random sample of size $n=84$.
Find the probability that a single randomly selected value is greater than 72.4.
$P\left(X>72.4\right)=$?
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SoosteethicU

Step 1
Given,
Mean $=49$
Standard deviation $=79.5$
Sample size $=84$
Step 2
Consider,
$P\left(X>72.4\right)=P\left(\frac{X-\mu }{\sigma }>\frac{72.4-\mu }{\sigma }\right)$
$=P\left(Z>\frac{72.4-49}{79.5}\right)$
$=P\left(Z>0.294\right)$
$=1-P\left(Z\le 0.294\right)$
$=1-0.6156=0.3844$ (From the standard normal table)
The probability that a single randomly selected value is greater than 72.4 is, 0.3844.

Jeffrey Jordon