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
ANSWERED
asked 2020-11-05

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.
\(\displaystyle{P}{\left({X}{<}{130.9}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Answers (1)

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
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