Question

# A population of values has a normal distribution with \mu=129.7 and \sigma=7.7. You intend to draw a random sample of size n=10.Find the probability that a single randomly selected value is less than 130.9. P(X < 130.9) =? Write your answers as numbers accurate to 4 decimal places.

Random variables

A population of values has a normal distribution with $$\displaystyle\mu={129.7}$$ and $$\displaystyle\sigma={7.7}$$. You intend to draw a random sample of size $$\displaystyle{n}={10}$$.
Find the probability that a single randomly selected value is less than 130.9.
$$\displaystyle{P}{\left({X}{<}{130.9}\right)}=$$?

2020-11-06
Step 1
Given Information:
$$\displaystyle\mu={129.7}$$
$$\displaystyle\sigma={7.7}$$
$$\displaystyle{n}={10}$$
Step 2
The probability that a single randomly selected value is less than 130.9
Firstly, z score will be determined.
$$\displaystyle{z}={\frac{{{x}-\mu}}{{\sigma}}}={\frac{{{130.9}-{129.7}}}{{{7.7}}}}={0.155}$$
By referring to the z distribution, the p-value at $$\displaystyle{z}={0}$$.155 is 0.438
Therefore, the probability that a single randomly selected value is less than 130.9 is 0.438