# A population of values has a normal distribution with \mu=154.5 and \sigma=96.1. You intend to draw a random sample of size n=134. Find the probability that a single randomly selected value is greater than 167. P(X > 167) =? Write your answers as numbers accurate to 4 decimal places.

A population of values has a normal distribution with $\mu =154.5$ and $\sigma =96.1$. You intend to draw a random sample of size $n=134$.
Find the probability that a single randomly selected value is greater than 167.
$P\left(X>167\right)=$?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Luvottoq
Step 1
A population of values has a normal distribution with $\mu =154.5$ and $\sigma =96.1$.
Step 2
X be a sample from the Normal distribution with $\mu =154.5$ and $\sigma =96.1$.
The probability that a single randomly selected value is greater than 167.
$P\left(X>167\right)$
$=1-P\left(X\le 167\right)$
$=1-P\left(\frac{X-154.5}{96.1}\le \frac{167-154.5}{96.1}\right)$
$=1-P\left(Z\le 0.13\right),asZ=\left(\frac{X-154.5}{96.1}\right)$ follows Normal(0,1)
$=1-\varphi \left(0.13\right),\varphi \left(0.13\right)$ calculated from Normal distribution table.
$=1-0.5517=0.4483$
Therefore, the probability that a single randomly selected value is greater than 167 is 0.4483.