Question

assume the random variable x is normally distributed with mean μ = 84 and standard deviation σ = 4. find the indicated probability. p(74 < x < 78) p(74 < x < 78)= (round to four decimal places as needed )

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$.
For $x = 74$, $z_1=\frac{74 - 84}{4}=\frac{- 10}{4}=-2.5$.
For $x = 78$, $z_2=\frac{78 - 84}{4}=\frac{-6}{4}=-1.5$.

Step2: Use the standard normal distribution table

We want to find $P(-2.5$P(-2.5From the standard - normal table, $P(Z < - 1.5)=0.0668$ and $P(Z < - 2.5)=0.0062$.

Step3: Calculate the probability

$P(-2.5

Answer:

$0.0606$