Question

for a normal variable x ~ n(μ = 50.7,σ = 5.1), find the probability p(44.75 < x < 56.85): p(44.75 < x < 56.85) = (round the answer to 4 decimal places) question help: video message instructor post to forum submit question

Explanation:

Step1: Standardize the bounds

First, use the formula $Z=\frac{X - \mu}{\sigma}$. For $X_1 = 44.75$, $Z_1=\frac{44.75 - 50.7}{5.1}=\frac{-5.95}{5.1}\approx - 1.17$. For $X_2 = 56.85$, $Z_2=\frac{56.85 - 50.7}{5.1}=\frac{6.15}{5.1}\approx1.21$.

Step2: Use the standard - normal distribution

We know that $P(44.75 < X < 56.85)=P(-1.17Looking up in the standard - normal table, $\varPhi(1.21)=0.8869$ and $\varPhi(1.17)=0.8790$.
$P(-1.17 < Z < 1.21)=0.8869-(1 - 0.8790)=0.8869 - 0.1210=0.7659$.

Answer:

$0.7659$