Question

for a normal variable $xsim n(mu = 91.9,sigma = 15.1)$, find the probability $p(x < 66.75)$: $p(x < 66.75)=square$ (round the answer to 4 decimal places) question help: video message instructor post to forum submit question

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$. Here, $x = 66.75$, $\mu=91.9$, and $\sigma = 15.1$. So, $z=\frac{66.75 - 91.9}{15.1}=\frac{- 25.15}{15.1}\approx - 1.6656$.

Step2: Find the probability from the standard normal table

We want to find $P(X < 66.75)$, which is equivalent to $P(Z<-1.6656)$ in the standard - normal distribution. Looking up the value in the standard normal table (or using a calculator with a normal - distribution function), $P(Z < - 1.6656)\approx0.0480$.

Answer:

$0.0480$