Question

assume the random variable x is normally distributed with mean $mu = 87$ and standard deviation $sigma = 4$. find the indicated probability.
$p(x < 79)$
$p(x < 79)=square$ (round to four decimal places as needed )

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 79$, $\mu = 87$, and $\sigma = 4$.
$z=\frac{79 - 87}{4}=\frac{-8}{4}=-2$

Step2: Find the probability

We want to find $P(x < 79)$, which is equivalent to $P(z < - 2)$ using the standard normal distribution table. Looking up the value in the standard - normal table, we find that $P(z < - 2)=0.0228$.

Answer:

$0.0228$