 # A population of values has a normal distribution with \mu=192.6 and \sigma=34.4. You intend to draw a random sample of size n=173.Find the probability that a single randomly selected value is less than 186.1.P(X < 186.1) =? Write your answers as numbers accurate to 4 decimal places. midtlinjeg 2021-02-13 Answered

A population of values has a normal distribution with $\mu =192.6$ and $\sigma =34.4$. You intend to draw a random sample of size $n=173$.
Find the probability that a single randomly selected value is less than 186.1.
$P\left(X<186.1\right)=$?

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Step 1
Given:
$\mu =192.6$,
$\sigma =34.4$,
$n=173$.
The Z-score follows standard normal distribution.
Step 2
$P\left[X<186.1\right]=P\left[\frac{X-\mu }{\sigma }<\frac{186.1-192.6}{34.4}\right]$
$=P\left[Z<-0.19\right]=0.4247$ (Use standard normal table)
The probability that a single randomly selected value is less than 186.1 is 0.4247.

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