Question

assume the random variable x is normally distributed with mean μ = 94 and standard deviation σ = 5. find the indicated probability. p(x < 81) p(x < 81)=□ (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 $x = 80$, $\mu=94$, and $\sigma = 5$.
$z=\frac{80 - 94}{5}=\frac{- 14}{5}=-2.8$

Step2: Find the probability

We want to find $P(x < 80)$, which is equivalent to $P(z<-2.8)$ using the standard normal distribution table.
Looking up the value of $P(z < - 2.8)$ in the standard - normal table, we get $0.0026$.

Answer:

$0.0026$