Question

assume the random variable x is normally distributed with mean μ = 84 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 $z=\frac{x-\mu}{\sigma}$. Here, $x = 81$, $\mu=84$, and $\sigma = 5$. So, $z=\frac{81 - 84}{5}=\frac{-3}{5}=- 0.6$.

Step2: Find the probability using the standard normal table

We want to find $P(X < 81)$, which is equivalent to $P(Z<-0.6)$ using the standard - normal transformation. Looking up the value of $P(Z < - 0.6)$ in the standard normal table, we get $0.2743$.

Answer:

$0.2743$