# 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.

Question
Random variables
Assume that there is a sampling distribution of $$\displaystyle\overline{{{x}}}$$ 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.

2021-02-26
Here, $$\displaystyle{X}\sim{N}{\left({45},{6.2}\right)}$$.
The probability that a randomly selected person has a value less than 40 is calculated as follows:
$$\displaystyle{P}{\left({X}{<}{40}\right)}={P}{\left({\frac{{{X}-\mu}}{{\sigma}}}{<}{\frac{{{40}-{45}}}{{{6.2}}}}\right)}$$</span>
$$\displaystyle={P}{\left({z}{<}-{0.81}\right)}{\left[{F}{r}{o}{m}\ {t}{h}{e}\ {s}{\tan{{d}}}{a}{r}{d}\ {\left\|{a}\right\|}{l}\ {t}{a}{b}\le,\ {P}{\left({z}{<}-{0.81}\right)}={0.2090}\right]}={0.2090}$$</span>
The probability that a randomly selected person has a value less than 40 is 0.2090.

### Relevant Questions

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