Answer:
The probability that a randomly selected student has a score between 350 and 550 is 0.5867
Step-by-step explanation:
We know that,
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
where,
Z = Z score,
X = raw score,
μ = mean,
σ = standard deviation,
The probability that a randomly selected student has a score between 350 and 550 is,
[tex]P(350<X<550)\\\\=P(350-500<X-500<550-500)[/tex]
[tex]=P\left(\dfrac{350-500}{110}<\dfrac{X-500}{110}<\dfrac{550-500}{110}\right)[/tex]
[tex]=P\left(-1.36<Z<0.45\right)[/tex]
[tex]=P(Z<0.45)-P(Z<-1.36)[/tex]
[tex]=0.6736-0.0869[/tex]
[tex]=0.5867[/tex]
