# Assume that there is a sampling distribution of \bar{x} of size 34 and they are selected at random from a normally distributed with a mean of 45 and a standard deviation of 6.2. Find the probability that 1 randomly selected person has a value less than 40.

Assume that there is a sampling distribution of $\stackrel{―}{x}$ of size 34 and they are selected at random from a normally distributed with a mean of 45 and a standard deviation of 6.2.
Find the probability that 1 randomly selected person has a value less than 40.
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Mitchel Aguirre

Here, $X\sim N\left(45,6.2\right)$.
The probability that a randomly selected person has a value less than 40 is calculated as follows:
$P\left(X<40\right)=P\left(\frac{X-\mu }{\sigma }<\frac{40-45}{6.2}\right)$

The probability that a randomly selected person has a value less than 40 is 0.2090.