Question

A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting 75 < X < 85

Answer 1

$P(75<X<85)=P(\frac{75-80}{10}<Z<{85-80}{10})=P(-0.5<Z<0.5)=$

$=P(Z<0.5)-P(Z<-0.5)=P(Z<0.5)-(1-P(Z<0.5))=$

$=2P(Z<0.5)-1=2*0.6915-1=0.3830.$