assume the random variable x is normally distributed with mean $mu = 86$ and standard deviation $sigma = 4$. find the indicated probability.
p(74

Question

assume the random variable x is normally distributed with mean $mu = 86$ and standard deviation $sigma = 4$. find the indicated probability.
p(74 < x < 81)
p(74 < x < 81)=
(round to four decimal places as needed.)

Accepted Answer

# Explanation:
## Step1: Standardize the bounds
We use the formula $z=\frac{x - \mu}{\sigma}$. For $x = 74$, $z_1=\frac{74 - 86}{4}=\frac{- 12}{4}=-3$. For $x = 81$, $z_2=\frac{81 - 86}{4}=\frac{-5}{4}=-1.25$.
## Step2: Rewrite the probability
$P(74 < x<81)=P(-3<z<-1.25)$.
## Step3: Use the standard - normal table
$P(-3<z<-1.25)=P(z < - 1.25)-P(z < - 3)$. From the standard - normal table, $P(z < - 1.25)=0.1056$ and $P(z < - 3)=0.0013$.
## Step4: Calculate the probability
$P(-3<z<-1.25)=0.1056 - 0.0013=0.1043$.

# Answer:
$0.1043$

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QUESTION IMAGE

Question

Explanation:

Step1: Standardize the bounds

Step2: Rewrite the probability

Step3: Use the standard - normal table

Step4: Calculate the probability

Answer: