# A population of values has a normal distribution with mean = 37.4 and standard deviation 77.4. If a random sample of size n=15 is selected, Find the probability that a single randomly selected value is greater than 53.4. Round your answer to four decimals. P(X > 53.4)=?

A population of values has a normal distribution with mean = 37.4 and standard deviation 77.4. If a random sample of size $n=15$ is selected,
Find the probability that a single randomly selected value is greater than 53.4. Round your answer to four decimals.
$P\left(X>53.4\right)=$?
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wheezym

The probability that a single randomly selected value is greater than 53.4 is 0.4168, which is obtained below:
$P\left(M>x\right)=1-P\left(M
$=1-P\left(z<\frac{x-\mu }{\sigma }\right)$
$P\left(M>53.4\right)=1-P\left(M<53.4\right)$
$=1-P\left(z<\frac{53.4-37.4}{77.4}\right)$

$=1-0.58317=0.4168$