Suppose x is a normal random variable with μ = 35 and σ = 10. find p(55.5 < x < 69.7).

Answer:[tex]\boxed{\boxed{P(55.5 < X< 69.7)=0.01992}}[/tex]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.So,[tex]=P(55.5 < X< 69.7)[/tex][tex]=P(55.5-35 < X-35< 69.7-35)[/tex][tex]=P(\dfrac{55.5-35}{10}< \dfrac{X-35}{10}< \dfrac{69.7-35}{10})[/tex][tex]=P(\dfrac{55.5-35}{10}< Z< \dfrac{69.7-35}{10})[/tex][tex]=P(2.05< Z<3.47)[/tex][tex]=P(Z<3.47)-P(Z<2.05)[/tex][tex]=0.99974-0.97982\\\\=0.01992[/tex]